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The Turing machine can compute anything that can be computed. It is the very definition of computation and the fundamental tool for reasoning about computers. You really need to know what it is all about.
Here are two useful articles from i-programmer to get you started:
|What is a Turing Machine?|
Of course, Wikipedia's own article on this topic is always worth a read.
Check out the following site as well which lets you trial an online/virtual Turing machine! Pretty cool: http://turingmachine.io/