This is the coding system used by the Germans during World War Two. The Germans thought it was unbreakable, but it was in fact cracked by Alan Turing and his team at Bletchley Park. The fact that it had been broken had to be kept secret if the Allied invasion of Europe was to be a success. So much so that the Allies knew about the German air raid attack on Coventry before it happened, but to give any warning about it would have raised suspicions on the part of the Germans who would have then changed the Enigma settings, making their communications unreadable during the invasion.
Enigma was a machine, consisting of a keyboard, rotors and lights. The machine was set to an initial setting, a key pressed and an electrical circuit completed through the three rotors resulting in one of the lights, each representing a letter, illuminating. The rotors then individually turned by a pre-determined amount before the next key was pressed. The internal wiring of the rotors gave 158,000,000,000,000,000,000 possible solutions. One of the few things known by the Allies was that the illuminated letter could not be the same as the letter pressed on the keyboard.
Although the Enigma Machine was though to be a German invention it was actually developed by the Dutch to communicate banking information. The Germans bought the patent in 1923 for intellegence purposes. Polish intellegence managed to purchase an Enigma at a Trade Fair and managed to get a code book from a French Agent. When Poland was occupied in 1939 they gave the information and the machine to the Allies.
By the end of the war 10% of all German messages were being read, having been decoded at Bletchley Park.
You can use The Village Interweb to play with an Enigma Simulator.