Term used in Role-playing Games to denote the worst possible dice roll for a given attempted action, usually with catastrophic (if not fatal) and entertaining results.

An example from AD&D (which happens rather frequently):

Drace is firing his bow from inside a group. He has a THAC0 of 19 and is tring to hit a goblin with an Armor Class of 7. Therefore, he needs to roll a 12 on a twenty-sided dice to successfully hit.

Unfortunately, he rolls a 1, which is a botch. Because of this, one or more of several things may happen, depending on the DM:

1. Drace simply misses, and may lose his next attack out of sheer incompetence or weapon fumbling.
2. Drace's bowstring snaps, rendering the weapon useless.
3. Drace misses his target, and hits someone/something else, possible a member of his own party. Make that probably.

The best description of a botch comes out of the HoL sourcebook and runs as follows:

Bob bends down to tie his shoe.
Bob rolls a botch.
Bob's head explodes.