A decision problem is a computational question that only ever has two possible answers: yes or no. Instead of asking a computer to produce a number or a list, you're asking it to check whether some input satisfies a certain property. Formally, a decision problem can be thought of as the set of all inputs for which the answer is "yes", and solving it means figuring out whether a given input is in that set.
A decision problem is decidable if there is an algorithm that will always finish running and give the correct yes/no answer, no matter what input you give. The important part is that it has to terminate: it can't get stuck in an infinite loop for some inputs. If no algorithm like that can exist, the problem is called undecidable.
P stands for "polynomial time". It's the group of decision problems that a computer can actually solve quickly, meaning the time it takes grows in a polynomial way as the input gets bigger, rather than exploding exponentially.
NP stands for "nondeterministic polynomial time". It's the group of problems where, even if finding a solution might take forever, checking whether a proposed solution is correct can be done quickly. Every problem in P also belongs to NP, since if you can solve something quickly, you can obviously verify it quickly too by just solving it yourself.
It's asking whether checking an answer is fundamentally easier than finding one. "P vs NP" question asks whether that gap is real or whether some undiscovered method could always let you find solutions just as fast as you can verify them. Most researchers believe P and NP are different, but nobody has ever managed to prove it either way.
At least $1,000,000. P vs NP is one of the seven Millennium Prize Problems named by the Clay Mathematics Institute in 2000, and each one carries a $1 million reward for a verified solution. If I proved P = NP with an actual working method, the real-world value would likely go far beyond the prize money, since it would mean that fast algorithms exist for huge numbers of problems we currently think are essentially unsolvable.