This is covered more completely in NpComplete, but briefly:

* A problem is NpHard if a solution to it would imply a solution to all NP problems. Problems that are both NP (NondeterministicPolynomial) and NpHard are said to be NpComplete.

* Examples of NP-Complete problems include the TravelingSalesmanProblem (TSP), KnapsackProblem, 3-Satisfiability, and hundreds more.

This falls in an area known as ComplexityTheory.