You have been chosen by you patron. This will be a powerful individual from the upper echelons of the imperial hierarchies. They could be an Inquisitor, a Commissar, or maybe a Rogue Trader - we'll be using player consensus and random dice to determine exactly who they are and what they want.
They have formed a team of operatives; seemingly ordinary imperial citizens, randomly generated and then tweaked by you the players to be your characters in this world. You could be fresh Guardsmen recruits, Adminstratum bureaucrats, novice tech priests - anyone unimportant will do.
Then the Patron will send you out on missions, which could be anything from infiltrating a hive gang, to checking a spaceport for smugglers, to retrieving a book from a library. If all goes well, you'll all make it back in one piece. If not, you may come back with fewer or more limbs than you expect. 

No knowledge of Warhammer 40k is required to play, since most citizens don't know much about their own universe anyway.