Settings from domain controllers (privileges etc) are propagated over the network to other servers (Email,File servers etc).
So when you authenticate against a DC (by logging into your workstation etc) you get a token back which can be sent to other hosts on the network who then understand what to grant access to based on that token.
This makes it easier for a large org with an international presence to allow say marketing teams in the London and New York offices to have access to the same files etc and be able to use each others workstations interchangeably whilst all being managed by the IT team in Mumbai.
This means that if you stick to mainly MS products you get the advantage of knowing that everything will integrate into AD so you spend less time handrolling shared authentication etc.
ADFS is hugely under-rated, and is arguably the most capable identity federation software out there because it's the only implementation I know of that does both passive- (browser-based), and active federation, which allows you to authenticate against AD from your JSON service.
That story gets even better with U-Prove (http://www.microsoft.com/mscorp/twc/endtoendtrust/vision/upr...).