According to Britannica, a decision problem is the problem of finding an algorithm or repetitive procedure that will always yield a definite answer, "yes" or "no" for any question of the class of mathematics and formal logic. The method consists of performing successively a finite number of steps determined by preassigned rules.
A decision problem that can be solved by an algorithm that halts on all inputs in a finite number of steps. In other words, a problem whose language is recursive is known to be decidable, otherwise, the problem is said to be undecidable. The algorithm that takes as input an instance of the problem and determines whether the answer to the instance is "yes" or "no". eg: Given a DFSM M and string w, does M accept w?
According to the website CodeCrucks, P problems are a set of problems which can be solved in polynomial time by deterministic algorithms while Np problems are problems which can be solved in nondeterministic polynomial time. We could come to the conclusion P stands for polynomial deterministic problems while NP stands for nondeterministic polynomial problems.
According to smashmagazine.com, P versus Np is a mathematical question masquerading as philosophical. It describes the difference between solving a problem a knowing whether you've solved it. So the question does P equal Np? This means if the solution to a problem can be verified in polynomial time, can it be found in polynomial time?
According to Gizmodo, if you can prove or disprove its cryptically short equation, you'd be a million dollars richer and maybe even billions of dollars richer depending on your scruples.