The Enigma was an electro-mechanical rotor cypher machine used for both encryption and decryption, widely used in various forms in Europe from the early 1920s on. It is most famous for having been adopted by most German military forces from about 1930 on. Ease of use and the supposedly unbreakable cypher were the main reasons for its widespread use. The machine had two inherent weaknesses: it guaranteed that a letter would never be encrypted to itself and the rightmost rotor would rotate a set number of places before the next would rotate (26 in the initial version). In German usage the failure to replace the rotors over many years of service and patterns in messages further weakened the system. The cypher was broken, and the reading of information in the messages it didn't protect is sometimes credited with ending World War II at least a year earlier than it would have otherwise.
The counterpart British encryption machine, Typex, and several American ones, e.g. the SIGABA (or M-134-C in Army use), were similar in principle to Enigma, but far more secure. The first modern rotor cypher machine, by Edward Hebern, was considerably less secure, a fact noted by William F. Friedman when it was offered to the US Government.
Enigma was developed by Arthur Scherbius in various versions dating back to 1919. He set up a Berlin company to produce the machine, and the first commercial version (Enigma-A) was offered for sale in 1923. Three more commercial versions followed, and the Enigma-D became the most important when several copies were purchased by the Reichsmarine in 1926. The basic design was then picked up by the Army in 1929, and thereafter by practically every German military organization and by many parts of the Nazi hierarchy. In the German Navy, it was called the "M" machine.
Versions of Enigma were used for practically all German (and much other European Axis) radio, and often telegraph, communications throughout the war; even weather reports were encrypted with an Enigma machine. Both the Spanish (during the Civil War) and Italians (during World War II) are said to have used one of the commercial models, unchanged, for military communications. This was unwise, for the British (and one presumes, others) had succeeded in breaking the plain commercial version(s) or their equivalents. This contributed to the British defeat of a large part of the Italian fleet at Matapan.
The Enigma machine was electro-mechanical, meaning it used a combination of electrical and mechanical parts. The mechanism consisted primarily of a typewriter-style keyboard, which operated electrical switches as well as a gearing mechanism.
The electrical portion consisted of a battery attached through the keys to lamps. In general terms, when a key was held down on the keyboard, one of the lamps would be lit up by the battery. In the picture to the right you can see the typewriter keys at the front of the machine, and the lights are the small (barely visible) circles "above" the keyboard in the middle of the machine.
The heart of the basic machine was mechanical, consisting of several connected rotors. Enigma rotors in most versions consisted of flat disks with 26 contacts on each side, arranged in a circular manner around the outer faces of the disk. Every contact on one side of each disk is wired to a different contact on the other side. For instance, in a particular rotor the 1st contact on one side of the rotor might be wired to the 14th contact on the other side, the 2nd one on the first side to the 22nd on the other, and so forth. Each rotor in the set supplied with an Enigma was wired differently than the others, and the German military/party models used different rotor wirings than did any of the commercial models.
Inside the machine were three slots (in most variants) into which the rotors could be placed. The rotors were "stacked" in the slots in such a way that the contacts on the "output" side of one rotor were in contact with the "input" contacts on the next. The third rotor in most versions was connected to a reflector (unique to the Enigma family amongst the various rotor machines designed in the period) which was hard wired to feed outputs of the third rotor back into different contacts of the third rotor, thence back to the first rotor, but by a different route. In the picture you can see the three stacked rotors at the very top of the machine, with teeth protruding from the panel surface which allow the rotors to be turned by hand.
When a key was pressed on the keyboard, current from the battery flowed from the switch controlled by that key, say A, into a position on the first rotor. There it would travel through the rotor's internal wiring to, say, the J position on the other side. It would then go into the next rotor, perhaps turned such that the first rotor's J was lined up with the second's X. From there it would travel to the other side of the second rotor, and so on. Because the signal had travelled through the rotors and back, some other letter than A would light in the lamp array – thus substituting one letter for another, the fundamental mechanism in all substitution cypher systems.
Because the rotors changed position (rather like an automobile odometer) with every key press, A might be Q this time, but the next A would be something different, perhaps T. After 26 letters were pressed, a cam on the rotor advanced the rotor in the next slot by one position. The substitution alphabet thus changed with every plaintext letter, and kept changing with every plaintext letter for a very long time.
Better yet, due to the "random" wiring of each rotor, the exact sequence of these substitution alphabets varied depending on the initial position of the rotors, their installed order, and which rotors were installed in the machine. These settings were referred to as the initial settings, and were given out in books once a month (to start with -- they became more frequent later on).
The most common versions of the machine were symmetrical in the sense that decipherment works in the same way as encypherment: type in the cyphertext and the sequence of lit lamps will correspond to the plaintext. However, this works only if the decyphering machine has the same configuration (i.e., initial settings) as had the encrypting machine (rotor sequence, wiring, alphabet ring settings, and initial positions); these changed regularly (at first monthly, then weekly, then daily and even more often nearer the end of the War on some networks) and were specified in key schedules distributed to Enigma users.