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In its simplest form, a Turing machine is composed of a "tape", a ribbon of paper of indefinite length. There is a "head" that can read the symbol, chose to write a new symbol in place, and then move left or right. The Turing machine is said to be in a certain "state". Finally, the program is a list of "transitions", that is a list that says, given a current state and a symbol currently under the head, what should be written on the tape, what state the machine should go, and whether the head should move left or right.
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