The Bombe was built by Alan Turing and others to assist in the cracking of German's Enigma code during World War 2.
It wasn't a computer [though the worlds first world's first programmable digital computer, the Colossus, was built by Tommy Flowers for use at Bletcley Park].
The Bombe cracked codes using fairly simple brute force methods. Wikipedia has a good article on the device.
A replica Bombe has been built and is on display at Bletchley Park.