In computational complexity theory, the complexity class NP-complete, also known as NP-C or NPC, is a subset of NP ("non-deterministic polynomial time"). Problems are designated "NP-complete" if their solutions can be quickly checked for correctness, and if the same solving algorithm used can solve all other NP problems. They are the most difficult problems in NP in the sense that a deterministic, polynomial-time solution to any NP-complete problem would provide a solution to every other problem in NP (and conversely, if any one of them provably lacks a deterministic polynomial-time solution, none of them has one). Problems in NP-complete are known as NP-complete problems. A more formal definition is given below.
One example of an NP-complete problem is the subset sum problem which is: given a finite set of integers, determine whether any non-empty subset of them sums to zero. A supposed answer is very easy to verify for correctness, but there is no known efficient algorithm to find an answer; that is, all known algorithms are impractically slow for large sets of integers.
Reference:
http://en.wikipedia.org/wiki/NP-complete
