A normal (deterministic) turing machine that has a "guessing head" - a write-only head that writes a guess at a solution on the tape first, based on some arbitrary internal algorithm. The regular turing machine then runs and returns "yes" or "no" to indicate whether the solution is correct.

A nondeterministic turing machine can solve nondeterministic polynomial time computational decision problems in a number of steps that is a polynomial function of the size of the input