Being battle forged means all of your units are in some sort of force organization chart of some sort (think of it as being 'bound' to the chart) Instead of needing to have 1
HQ and two troops, every army has to have at least 1 chart. Thats what a detachment is. Each detachment will have its own force organization chart, may have some restrictions on what units are allowed to be 'bound' to it, and might give you some benefits for having used it. The force organization chart you are most familiar with is
REQUIRED
1 HQ
2 TROOPS
OPTIONAL
1 HQ
4 TROOPS
3 ELITES
3 FAST ATTACK
3 HEAVY SUPPORT
This chart was used for every army before 7th edition came out. Every army can still use this chart if they want but are not required to any more. This chart now belongs to a detachment called the "Combined Arms Detachment" or
CAD for short. The only restriction to what kind of units can be bound to this chart is that each unit bound to this chart must have the same faction. Its benefits are explained in the
40k rulebook. You can have a battle forged army and not use the combined arms detachment. There are several alternatives, depending on your faction. For Example the Inquisition faction has one that is
REQUIRED
1 HQ
OPTIONAL
1 HQ
3 ELITES
You can think of detachments as mini armies. The restrictions and/or benefits of any detachment only applies to the units bound to its chart and no unit is allowed to be in more then one detachment at a time. Its important to mention that because you can have more then one detachment and having more then one detachment is actually very common in 7th edition. Regardless of the number of detachments you have, one of them will be your 'primary' detachment. Your primary detachment is which ever detachment your warlord is 'bound' to.
Formations are a special kind of detachment. Instead of having a force organization chart with slots that you fill, it will have a list of what specific units must be in the formation and hat units can be in the formation. Looking at them they look more like 'super units' than armies, but don't be fooled they stand on their own just like any other detachment (and that also means units in a formation cannot also be in a detachment) . In terms of making sure your army is all bound to some kind of chart, you can think of this list like a chart and the units listed are all bound to it. Now you might be thinking "But that means I can have a battle forged army with just one formation" and you are right.
What the hell is a 'Derucon' detachment? Starting with codex Necrons
GW introduced what like like to call "Umbrella Detachments" but most people on the net call them Derucon detachments because that was the name of the very 1st one. These umbrella detachments are not made up units, but instead are made up of other detachments (usually formations). A unit that is part of a detachment/formation that is in tern part of one of these umbrella detachments is actually part of both (I know, we said that wasn't allowed but this is an exception.) and will receive the benefits of both. Just about every codex since Necrons has had its own version of umbrella detachments, each with its own little quirks.