The Free On-line Dictionary of Computing (30 December 2018):

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

   (1995-04-27)