The Fat Man is a handheld tactical nuclear catapult found in various places in Fallout 3.
Because of its nuclear payload, it is by far the strongest V.A.T.S. enabled weapon in the game, perfect for taking out multiple enemies or heavily armored units - and in normal use, you'll be encountering both. The Fat Man has an estimated range of 150+ yards and will fall if shot in the air; be aware that the blast zone will be irradiated.