Brainfuck is a simple turing-machine based language. It's also a turing tarpit - a language that is turing complete but just about impossible to write useful programs in. It's operation is incredibly simple - imagine you have an infinite length of tape where each square contains a number. You have a "head" that sits on one of the squares. The commands are as follows:

< : move the head left one square
> : move the head right one square
+ : increment the head square
- : decrement the head square
. : print the head square
\ : get a character from standard input
[ : while the head square is not zero do
] : end [ block

and that's all. The awesome part about this simplicity is that each command can be mapped exactly to a piece of c code. This is a simple implementation of this which converts each symbol to a piece of c code.