A Turing machine is an abstract computing device.

It consists of:

a tape which contains a series of 1 or 0.

a read/write head which can move to the left or to the right along the tape.

a table of instructions.

The machine starts in a given state and reads the first symbol (a 1 or a 0).
According to the table of instructions and the state the machine is in, the device might:

write a 0 or a 1.

move to the left or right.

go to a new state (defined in the table of instructions).

A Turing machine is more like a computer program than a machine.
Computer scientists and logicians have shown that Turing machines -- given enough time and tape -- can compute any function that any conventional digital computers can compute

The next page contains a java applet designed by Graham Stalker-Wilde which illustrates how a Turing machine works.