There is a great deal of excellent material about Turing and his ideas on the Web, which is not surprising given that he is one of the progenitors of modern computing science. A longer, very readable version of the description given here is found in a book chapter called Tools For Thought by Howard Rheingold, which I in part am paraphrasing (with the permission given at that Web site).

Perhaps the easiest way to track down most Turing-related links is at the Alan Turing Home Page that is maintained by Andrew Hodges, author of "Alan Turing: The Enigma. (Turing himself died in 1954, a suicide.) Among many other topics, the Turing Machine is discussed and links to on-line simulations are provided. A good, brief introduction to the Turing Machine is in a Stanford On-line Encyclopedia of Philosophy entry.