(Quick overview from Wikipedia):
The relationship between the complexity classes P and NP is an unsolved question in theoretical computer science. It is considered to be the most important problem in the field – the Clay Mathematics Institute has offered a $1 million US prize for the first correct proof.
In essence, the question P = NP? asks: if 'yes'-answers to a 'yes'-or-'no'-question can be verified "quickly" (in polynomial time), can the answers themselves also be computed quickly?
