Wikipedia
NP-hardness ( non-deterministic polynomial-time hard), in computational complexity theory, is a class of problems that are, informally, "at least as hard as the hardest problems in NP". More precisely, a problem H is NP-hard when every problem L in NP can be reduced in polynomial time to H. As a consequence, finding a polynomial algorithm to solve any NP-hard problem would give polynomial algorithms for all the problems in NP, which is unlikely as many of them are considered hard.
A common mistake is thinking that the NP in "NP-hard" stands for "non-polynomial". Although it is widely suspected that there are no polynomial-time algorithms for NP-hard problems, this has never been proven. Moreover, the class NP also contains the set of P in which all problems can be solved in polynomial time. NP in fact stands for "Nondeterministic Polynomial time."