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Just read a article on BOL and mentioned the above lists, i was curious is someone could help me out and explain it to me.

Thanks in advance.

Deathstar lists are lists that include a certain powerful "Deathstar".
Deathstar is an elitistic unit that is often extremely tough to kill, deals lots of killing power and usually costs like a house in Tinseltown.

Examples:
Seer Council
Big unit of TH/SS Terminators with Corbulo in LR
Smashf***er with bunch of Gravy-bikes

EDIT:
Note that the Deathstar isn't necessarily a top-tier instant-win unit.
Those are the most common ones, but even less competitive options can fulfill the requirements (such as the previous Termie example)

The beast start list is a dark eldar list with eldar allies and it is a large amount of beasts with the baron and a farseer attached to it. The squad and it turns into a nightmare if the farseer gets fortune.

Deathstar lists can be countered if you use escalation as D weapons ignore most of its shenanigans.

99% of lists that fall into that category are basically derived from the template below. Then there's the O'Vesa Star, Gravstar, Farsight Bomb, Screamerstar and White Scars Command Bikestar

Seerstar:

- Farseer on Jetbike with Shard of Anaris
- Farseer on Jetbike
- DE HQ Baron Sathonyx + 5 Kabalite Warriors
- 8-10 Warlocks on Jetbikes
- 5 man units of Dire Avengers in Wave Serpents OR
- 3 man WJB Squadrons as troops
- Wraithknights as support if you chose the WJBs

Beaststar:

- Farseer on Jetbike with Shard of Anaris
- Eldrad Ulthran or 2nd Farseer on Jetbike
- DE HQ Baron Sathonyx + 5 Kabalite Warriors
- DE Beastpack with 5 Beastmasters and 20-25 Khymerae
- 5 man units of Dire Avengers in Wave Serpents OR
- 3 man WJB Squadrons as troops
- Wraithknights as support if you chose the WJBs
- more often than not, a squad of Warp Spiders or Swooping Hawks

...hope this helps. Let me know if you need more info!