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Here is some fluff for a character for my own space marine army that i made. Chief admiral is the equivalent of a chapter master. Please write what you think of it. By the way the rules for this character can be found in 40k proposed rules!

Chief Admiral Ka'Vela of the Serpent Warriors

Ka'Vela started out as a Tactical Squad Sergeant in the Serpent Warriors' 7th Company. Tyranid Hive Fleet Mephitic was on the verge of an assault on his home planet, Minartus, and the reserves were ready for a call up at any time.
The campaign began. Two decades into the war, the Space Marines just about holding off the attack, Tactical Squad Ka'Vela was sent into action. Their orders were to guard an ancient temple, where the chapter's history lay, and to do everything they could to save it from harm. If the history was lost, the chapter would almost certainly fall.
For quite some time, nothing came, but as the Tyranids started to swarm across the planet, they were soon under attack. A single brood of Genestealers approached, nearly one hundred strong. That wasn't so bad, as the worst was still to come. They managed to shoot down every last one with penetrating bolter fire.
More came, again one hundred strong. They beat them down. Genestealers kept coming and gradually Ka'Vela and his men were running out of ammunition. Already one casualty had been taken, they couldn't allow any more to follow suit. They would have to battle hard.
Once more a group of Genestealers appeared on the horizon. Ka'Vela took out his binoculars. He looked through them, towards the Tyranids. They were led by a formidable Broodlord. This had to be the last group, if their general was coming with them. It must have sent out Tyranids to try and kill them off, and then decided to come with the last bunch of them. And again, the number of foes was around one hundred. Possibly one hundred Genestealers heading closer and closer to them at a tremendous pace. Very soon they were in range of the bolter fire. They made sure they did not waste bullets, every round counted. The flamer marine sprayed fire into the enemy lines, disrupting the horde ever so slightly, but doing enough. The bolter fire was not enough, though. The Tyranids were getting closer, their leader still in their midst. They had cut down the mob by a substantial amount, but Ka'Vela and his squadron knew that they would have to face up to the aliens in combat. Ka'Vela took his last magazine and put it not in his bolter (which he slung onto the floor) and instead into his bolt pistol. He drew his chainsword. He was ready for the worst. He was ready for the chapter's downfall.
The Genestealers jumped into the air, slashing their arms in the general direction of the marines. Tactical Squad Ka'Vela had their combat knives ready and the carnage began. Almost immediately one of the marines was wiped out by the Broodlord. Now Ka'Vela knew how powerful it really was. The battle progressed, the marines seemingly on top, fending off the Nids where they could. Ka'Vela would slice with his chainsword and shoot with his pistol. Soon, Ka'Vela was faced with the Broodlord. They fought hard, neither of them showing any mercy, and how could they? They were born enemies, not great friends. After a long struggle, Ka'Vela came out on top. The remaining Genestealers either fled or started to fight amongst themselves, which the Space Marines completely ignored. They had only lost two men in that horrible onslaught. Not bad for a Tactical Reserve Squad. They were rather satisfied with the outcome.
One of the men took out his communication devise, telling the 7th Company Captain that they were successful in their mission and the details that went along with it. The Captain listened and told them that he would send for another Reserve Squad to replace them. However, the whole squad was soon silenced. A roar came from the mountains not far from where they were then. Ka'Vela knew that roar. He knew the creature that made it. A Carnifex. It quickly came into view. Two giant crushing claws and two even larger and longer scything talons. A fearsome monster to say the least.
Again the squad got ready for a second engagement. They had literally no ammunition left, apart from Sergeant Ka'Vela's three rounds in his bolt pistol. He was unsure of how much damage it could really do. His hearts thumped in his chest and he could almost feel it beating against his armour. He was nervous, but ready. Nervous, but ready.
A good thing for the marines was that the Carnifex had no long range weapons, which could become fatal from the smallest of wounds. However that did not make the situation any easier, they were still battling a Carnifex, alone.
Once in range, Ka'Vela took his three shots with ultimate precision. It was very close, and he had managed to impair one of the talons. It could be used no more. He threw the bolt pistol to the floor. He concentrate all of his force and blows to the chainsword. Each man formed part of a circle around the Carnifex, confusing it somewhat. Each jabbed at different times, injuring several parts of its body. The Carnifex would occasionally strike out itself at some of the men, easily pushing against the front of the temple. It even managed to pick one up in its claw and crush it in front of everyone's eyes. It then focused on Ka'Vela. He swung and chopped away at the monster, but could not seem to break its exoskeleton. The Carnifex swiped at him him and he soon found himself lying on its back. It raised the crushing claw. It roared in pain. His last three men had worked out a weak point and stabbed hard into that exact area. It fell to the floor beside Ka'Vela who was helped up his colleagues.
Eventually, once the next squad took up the post, the remains of Tactical Squad Ka'Vela was taken to the main headquarters for the Space Marines involved in the campaign. They were taken to Captain Ba'Leta of the 7th Company, as that was the company to which they belonged. Once there, the four men were told that, after their valour that they had shown in battle, and their loyalty to their chapter, they would be promoted to the squadron of Company Veterans, in which Ka'Vela would be the Sergeant. They were joined by six other worthy marines and were now sent to the front line to be part of the defence of the great city of Agetor with one of the battle companies and half of another. They were very soon under siege.
The Tyranid attack was led by a Hive Tyrant and consisted of all sorts of monstrosities including Gargoyles, Termagants, Hormagaunts, Warriors and many more. The Captain of the full battle company raised his power sword and shouted commands at the top of his voice. His command squad were close by and collected inside a Razorback. The Devastator Squads on the turrets of the outer walls of the city fired their weapons, and the marines below did the same. The Tyranids fought back. All sorts of poisonous and toxic material was launched at the marines, many of them becoming casualties. Veteran Squad Ka'Vela got into their Rhino and set off. They could hear the roar of battle from outside, but managed to remain in full concentration, something every Serpent Warrior had to know how to do.
They exited the transport and could see the Captain and his Command doing the same thing to their left. They ran forward into battle. Ka'Vela, after being made Veteran Sergeant, had exchanged his bolt pistol for a plasma pistol and intended to bring down some Tyranids as he used it. The fight was long and hard and within a few days, the number of men in Veteran Squad Ka'Vela had been cut down and separated into two groups by order of the Captain. Ka'Vela was put with three others, his friends from the guarding of the temple, and another four Veterans were sent off on their own to carry out a certain mission, of which Ka'Vela was unsure of the exact details.
He and his men had been told to wipe out as many Tyranids as they could to protect the city. They knew they had to, it was their duty and others were also risking their lives for the city, so they should also. Within one month of the split off, Ka'Vela was then broken off from his men during a fight with a clump of Gargoyles. He was sheltering from the fire of the Tyranids behind his destroyed Rhino when he saw something atrocious. The Chapter Banner Bearer was about to be almost certainly killed by a Venomthrope. There would be no way to save him. But the banner had to be, no matter what the circumstances. Ka'Vela left his shelter and darted towards the Banner Bearer. He left his chainsword in its scabbard, he'd need a free hand. He dodged and ducked the flaying arms of the Tyranid savages. The banner was falling to the floor as the bearer was lifted by the Venomthrope's tentacles. Ka'Vela jumped in the banner's direction. He caught and stumbled across the rocky ground, carefully keeping the banner aloft. As soon as he could he stood upright. The Venomthrope turned towards him, dropping the bearer from its grasp also. The marine's body was covered in horrible slime that had been produced by the Tyranid. Underneath his helmet, he smiled and he then raised his left arm, which was holding his plasma pistol. The Venomthrope approached, seemingly unaware of the danger. Ka'Vela shot. The ball of plasma hit the Venomthrope right in the head, that was dead. But as the ball left the pistol, its temperatures raised so much that it exploded, taking his left hand with it. The pain was excruciating and he cried out like a tortured daemon.
Nevertheless, Ka'Vela managed to get past the pain, and turned back to get back to a hospital and to hand over the banner to someone in good condition. But as he did so, he was suddenly stopped in his tracks. Out of the ground formed a Mawloc, which was at least five times larger than himself. It screeched a terrible scream, and as it did so, poisonous spit hurtled towards him at a fast pace and he only just managed to dodge it. It stared down at him, and he stared back up with the same, stern expression. He knew exactly what to do.
He threw the banner into the air with as much force as possible and drew his chainsword. He then flung it at the creature. He got it straight in its sensor, the weak point. It was disorientated. And that was its downfall. As it leant back to attack, it went too far and fell back into its own tunnel. It was surely dead, the tunnel of a Mawloc was incredibly deep. Ka'Vela caught the banner as the Mawloc fell into the pit, and carried it back to the city, victorious.
After that battle with the Tyranid forces, Veteran Sergeant Ka'Vela was again promoted, but this time to Company Champion, his devotion to the Serpent Warriors was great and the Captains could not overlook it. He was given a replacement hand which was made of some of the strongest, yet lightest metal that could be found. He was also given a power sword after the loss of his chainsword in the fight against the Mawloc and decided to never use a plasma pistol ever again. He replaced that with a bolt pistol. He was very pleased with himself. He was Company Champion for around four decades, and the campaign still raged on. He was commissioned to become the Captain of the 7th Company (in the Serpent Warriors chapter Company Champions would always replace the Captains of a certain company, it was had always been that way throughout their history) after he had been brutally killed in a horrific onslaught with he and his Command Squad versus a brood of over thirty Ravenors. Ka'Vela had only just come out with his life and was the lone survivor.
Ka'Vela was then issued with a hand flamer instead of his bolt pistol. It was a useful weapon that was loved by the Serpent Warriors as it was a good way of softening up the foe. He was a brilliant Captain, and most agreed. He could easily motivate his men when they were in the most awful situations. But he still had a bigger part to play in the chapter's history. There was still the Battle of Tuscan.
Tuscan was the name of the tallest volcano on the planet and where the largest battle seen by the Serpent Warriors took place. Captain Ka'Vela took hold of his whole company. This battle saw the whole of the chapter fighting against the whole of the Hive Fleet Mephitic is a colossal brawl where the fate of both sides hung from a string. The action lasted for at least one year, if not longer. On its final day, Ka'Vela and some of his men were backing into the rocky insides of Tuscan, being attacked by a handful of deadly Lictors. As it seemed like the shaft inwards was never-ending, Ka'Vela heard something from above. It could only mean one thing. He turned and ran along the passage, ordering his men to do the same. None heard him and as he turned to see who had followed, he instead saw rocks piling down. He went up to the rocks, taking off his helmet and tried to hear any thing from the other side. He could. He heard screams of dying marines, men trying to escape any way possible. They had no chance, they would die. And so would he. There was no way out.
Even so, he continued towards what could be light, though he saw none of it for quite some time. When he did so, he reached a long, narrow ledge that reached the middle of the crater he was in, molten lava flowing below him. It was not supported well at all. And then he saw it ahead of him. Chief Admiral (the equivalent of a chapter master in the Serpent Warriors, they are very independent) Ro'Bala was in the middle of a duel with the leader of the Hive Fleet, the Swarmlord. Ro'Bala's power sword was doing wonders, but he needed help. That was where Ka'Vela came in. He raised his own sword and ran into the fight. They battled together as if they had known each other for years. They were unbelievable. But there had to be an end. No matter what they tried, the Swarmlord would not die. Suddenly, without notice, the Swarmlord lashed out at Ka'Vela and hit him against the back of the mountain. His power sword shattered, but he was not in terrible condition, he'd been worse. Then Ka'Vela watched as Ro'Bala lurched at the Tyranid and it fell backward, down into the lava, carrying the Chief Admiral with it. Ka'Vela ran to the edge of the ledge and just saw the last of Ro'Bala sink below the surface of the lava. All of a sudden he heard the ear-piercing growl of the Swarmlord as it too passed away.
Ka'Vela soon called for help and got it in the shape of a Land Speeder that collected him and the remains of his power sword. He was told that after the scream of the Swarmlord, the rest of the Tyranids either ran off or fought amongst themselves, like at the temple. Once back at the headquarters of the campaign, that was now over, he told the story of the death of Ro'Bala and the Serpent Warriors' Captains elected a new Chief Admiral. It was Ka'Vela after his brilliant efforts during the campaign. Ka'Vela, using the shattered power sword, forged a new blade, which he attached to a staff to create a power spear and mounted his hand flamer onto his forearm armour, the spear was a two-handed weapon. Ka'Vela still reins as Chief Admiral of the Serpent Warriors in the forty first millennium, and is one of the most successful the chapter has ever seen.

For background fluff this is pretty detailed... probably too detailed.

what do you mean, should it only be a short summary?

It can be long but you seem to have mixed a background description (like one you migth find in a codex) with a short story (like you might find in a Bl novel)
If you are just making a character you need tone down the story elements.