What's a Turing machine?

Question

What is a Turing machine and why do people keep mentioning it? My IBM PC is all I need to do my computation! Why does anyone care about these machines?

Answer 1

In addition to the Wikipedia entry, you might want to pick up the book The Annotated Turing by Charles Petzold. Subtitled "A Guided Tour through Alan Turing's Historic Paper on Computability and the Turing Machine", it includes the complete paper, broken into chunks with lots of discourse on the topic, including a historical perspective.