There are several conflicting stories of how the Allies got hold of information about the coding machines - see Enigma for these stories.
The incoming signals from the German war machine (more than 2,000 daily at the war's height) were of the highest level, even from Adolf Hitler himself. Such information enabled the Allies to build up an accurate picture of enemy plans and orders of battle, forming the basis of war plans both strategic and tactical.
The Allies were desparate to conceal from the Axis? command that they had broken Enigma. This was to the extent that although they had intercepted and knew of the whereabouts of U-boats lying in wait in mid-Atlantic, often convoys were allowed to sail into their midst for fear of alerting the Axis to their knowledge.
Usable Ultra intercepts of signals came too late to be of great help during the [Battle of Britain]?. It was not until the construction of electro-mechanical Bombes? and Colossus? that useful and timely intelligence was gained. Signals between Adolf Hitler and General [Günther von Kluge]? led to the destruction of a large part of the German forces in Normandy in 1944 after the Allied landing. In the Pacific the Germans had supplied their Japanese ally with an Enigma machine as early as 1937 [it is not at all clear that this happened. The Japanese could have (and probably did) buy a commercial version of the Enigma which, except for the plugboard and the actual rotor wirings, was essentially the German military machine]; the modified Japanese version, called "Purple" by the Americans, was duplicated by the [U.S. Signal Intelligence Service]? well before [Pearl Harbor]?. [Actually, the Japanese Purple machine ('alphabetic typewriter B') was an outgrowth of an earlier Japanes design the SIS called Red and was not an outgrowth of the Enigma or similar rotor machines; it treated vowels differently than consonants and used no rotors -- it used stepping switches instead. One of the reasons it was cryptanalytically vulnerable was that the key scheduling was poorly done]. Resultant revelations of Japanese plans led to U.S. naval victories in the battles of the [Coral Sea]? and Midway?, crushing the offensive power of the Japanese fleet, and enabled American flyers to find and shoot down the plane carrying Admiral Yamamoto Isoroku, the Japanese commander in the Pacific in April 1943. [Actually all of these things resulted from American (and possibly British, though this is less clear) breaks into the Imperial Navy's chief high level system, called by the Americans JN-25. It was regularly changed throughout the War, but after Pearl Harbor, the Americans were able to more or less keep up. Purple carried only diplomatic information -- very valuable, of course -- but carried no military tactical information at all.]
For 29 years after the war the existence of Ultra remained an official British secret. The ban was not lifted until 1974, the year that a key participant in the Ultra project, [Frederick William Winterbotham]?, published [The Ultra Secret]?. [Wintherbotham's book is very interesting, but is in error on many points. He worked in the distribute the Ultra to end consumers side of the operation and, based on the evidence of his book, did not understand much about cryptography. Peter Calvocorressi's book is better written and more responsible. He was involved in Bletchley Park's intelligence analysis of decrypted traffic and fit between the codebreakers and the distribution operation.]
A version of this story is told in the novel "Enigma" by [Robert Harris]?, ISBN 0804115486 (amazon.com, search). See also S Budiansky's "Battle of Wits" for a responsible account including much of recently declassified information about WWII cryptography.
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