NP-Complete problems are a class of problems in computational complexity theory that are both in NP and as hard as any problem in NP, meaning that if any NP-Complete problem can be solved efficiently, then every problem in NP can be solved efficiently. They are central to understanding the limits of what can be efficiently computed, and no polynomial-time algorithm is known for any NP-Complete problem, making them a key focus in the study of P vs NP problem.