Nondeterministic Turing Machine
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