NP-complete refers to a class of problems in computer science that are both in NP (nondeterministic polynomial time) and as hard as the hardest problems in NP. This means that if a solution can be verified quickly, finding that solution may not be quick. If any NP-complete problem can be solved quickly (in polynomial time), then all problems in NP can also be solved quickly. This leads to the famous P vs NP question, which asks whether every problem whose solution can be verified quickly can also be solved quickly.