NP-Completeness is a concept in computer science that helps classify problems based on their difficulty. A problem is considered NP-complete if it is both in the class 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, it implies that 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 quickly verified can also be quickly solved.