In complexity theory, NP ("Non-deterministic Polynomial-time") is the set of decision problems solvable in polynomial time on a non-deterministic Turing machine. Or, equivalently, YES answers are checkable in polynomial time on a deterministic Turing machine given the right information.
A language L belongs to NP if there exists a two input polynomial time algorithm A and a constant c such that
L = {x in {0,1} | ∃ certificate, y with |y| = O(xc) such that A(x,y) = 1}
