The game plays out in first person, as if it were a shooter game. The difference is that instead of weapons like pistols, shotguns, or machine guns, you have a mop, latex gloves, and a bucket. Your only enemy: Mess.
Because of the massacre (which you don't see), almost the entire ship is full of blood stains, guts, and human remains. To clean up the puddles of blood you'll need the bucket and mop; to get rid of the intestines and amputated appendages you'll need a trash can.
Viscera Cleanup is the closest thing to a space janitor simulator that you'll ever see in your life. Even though in itself the task of cleaning floors may not seem particularly fun, before long you'll discover that exploring the ship is in fact quite entertaining.