The video introduces the concept of NP completeness, explaining that solving just one of the thousands of unsolved math problems linked to it could unlock unimaginable advancements in technology, security, and optimization. Some of these problems, referred to as NP-complete, have practical applications such as organizing parties, finding optimal hospital locations, and predicting protein folding. The video demonstrates the limitations of the brute force algorithm to solve the Clique problem, which is a famous NP-complete problem. It then delves into the groundbreaking work of Stephen Cook and Leonard Levin, who revealed the deep connection between a famous NP problem called SAT and computation, showing that the SAT problem could carry out computation. The video discusses the technique of reduction, which is used by computer scientists when faced with a new hard problem, and how it can be quite technical. The question of whether P equals NP remains the biggest open question in computer science, as it would imply a huge shift in world view if it were proven.