Short for Big Fucking Gun 9000, the BFG was the biggest and baddest piece of demon slaying hardware you could get your hands on in DOOM and its sequel DOOM2.
It was very difficult to use effectively, unless you understood how it worked. The BFG9000 is without a doubt the weirdest weapon in the story of FPS games, and were it not for the fact that the DOOM source code has been released under the GPL, the workings would probably still be a complete mystery.
So how does the damn thing work?
The BFG deals two kinds of damage - direct hit and blast area. The direct hit damage is easy to figure out, you fire the BFG, the big green plasma ball hits something and deals it anywhere between 100 and 800 points of damage (the damage is random).
The Blast Area Damage is where things get interesting. After the green plasma ball detonates, and after the damage is calculated and deducted from the target that received the direct hit (if any), the area effect of the BFG is calculated. Targets that fall within a specially defined area will take varying amounts of damage.
Simply put, the blast area is like an imaginary 'cone' or 'fan' of 20 damage traces that briefly extends outward from the attacking player. The cone always points in the direction that the weapon was fired. For instance, if you originally fired the weapon in the northwest direction, the cone will always face northwest, regardless of which direction you're facing at the moment of detonation.
The perfect way to demonstrate this is to load up the good old map01 in DOOM2 in deathmatch mode along with a friend. Have your friend stand on the ledge where you begin the game in single player and place yourself so you are in the hallway that connects the starting room with the plasma rifle room.
Now, position yourself so that you can see the plasma rifle directly in front of you, and have the small rocket launcher room to your left.
Then, fire the BFG at the plasma rifle, and as soon as big green plasma ball appears and flies down the hallway, strafe right as quickly as you can, and stop when your friend is in the center of your view.
Now, if you did this right, the green plasma ball will hit the wall in the plasma rifle room just after your friend comes into view. The ball detonates, and BOOM! the blast effect is calculated, and since your friend is within the blast area cone he is now killed. Even though the BFG shot landed in an entirely different room.
Pretty FUBAR until you figure it out, but after that you'll be a friggin' BFG guru.
I got this info from The BFG FAQ v1.3, available at http://www.gamers.org/dhs/helpdocs/bfg_faq.html