Short answers, pulled from the story.
The Bombe was an electro-mechanical device used by British cryptologists to decipher German Enigma-machine-encrypted messages during the Second World War. It worked by systematically eliminating possible rotor settings until it found one that did not produce a logical contradiction, indicating a candidate solution for that day's Enigma configuration.
Alan Turing produced the initial design of the British Bombe in 1939 at Bletchley Park. Gordon Welchman added a critical refinement in 1940, the diagonal board, which exploited the symmetry of the Enigma's plugboard to vastly increase the machine's effectiveness.
The diagonal board was an attachment devised by Gordon Welchman that exploited the self-inverse symmetry of the Enigma's plugboard to eliminate far more candidate rotor settings per run. It was incorporated into the second British Bombe, Agnus Dei, which was working by the 8th of August 1940.
The four-rotor naval Enigma, called Triton by the Germans and Shark at Bletchley Park, became official in February 1942 and immediately ended the Allies' ability to read U-boat traffic. During the resulting Second Happy Time, German submarines sank 216 ships off the United States east coast between January and March 1942.
The US Navy Bombe's fast drum rotated at 1,725 revolutions per minute, 34 times the speed of the early British bombes. A three-rotor run took about 50 seconds on the US Navy machine, while a four-rotor run took about 20 minutes.
About 50 bombes were retained at RAF Eastcote after the war and the rest were destroyed. The surviving machines were possibly used against Eastern Bloc ciphers. In 1994 a working replica was begun; it won an Engineering Heritage Award in March 2009 and is now displayed at the National Museum of Computing at Bletchley Park.