NP-Complete is a classification in computer science that describes a set of problems for which no efficient solution is known, but if a solution is provided, it can be verified quickly. These problems are part of the larger class known as NP (nondeterministic polynomial time). If any NP-Complete problem can be solved quickly, it would imply that all problems in NP can also be solved quickly. The significance of NP-Complete problems lies in their complexity and the challenge they present. Examples include the Traveling Salesman Problem and Knapsack Problem. Researchers study these problems to understand computational limits and to develop algorithms that can handle them more effectively.