Apparently, a guy named Amherst taints some $20's with smallpox and puts them into circulation on Black Friday in New York. The "Dollar Flu" spreads quickly because the virus was changed and people died much quicker. Chaos ensues and rioters have taken over much of the city. The Division (the group called The Division) is sort of the last line of defense and are activated only when all other assets (US Military, Guard, Reserves, etc...) are wiped out. Additionally it looks like some of the group has gone rouge. A HQ is set up that has 3 wings; tech, medical, and security. In the game, you complete missions to get credits that start up components of the 3 wings. Like the rioters have taken some hostages. Clearing them out and freeing the hostages gets you 60 credits for Tech. Get enough credits and you can start up their counter-intel branch for example.
There is also a dark zone. Not sure what it is all about.