Possibility is a circumstance's ability or inability to exist. There are three, erm, possible ways to describe the possibility of any circumstance: possible, impossible, and certain. These terms are closely related to probability theory, which attempts to provide more rigorous measurements of possibility. Specifically, the impossibility of an event in probability theory is represented by "0" or "0%", whereas certainty is represented by "1" or "100%".
Although the notion of possibility plays a central role in many activities, its nature isn't well understood outside of common applications. For example, among the laity, any discussion of the existence of possibility, the possibility of possibility, or its relevance in our everyday lives would likely descend into mindless gobbledegook. Luckily, such esteemed philosophers as Saul Kripke and Gottfried Leibniz have clarified the matter for non-philosophers. It has been suggested by Leibniz and formally stated by Kripke that modal terms such as "possibly" and "necessarily" ought to be understood in terms of possible worlds. A possible world is a set of circumstances that may coexist. In other words, no possible world consists of things which are inconsistent when taken together, and so they are all logically possible.
Since a possible world is essentially any logically consistent scenario, there are infinitely many such worlds. Modal logicians such as Kripke contend that a circumstance is possible if it exists in at least one possible world, impossible if it exists in no possible worlds, and necessary if it exists in all possible worlds. While appealing to some, this conception of possibility offers no method of determining whether a given circumstance is compatible with the infinite number of worlds that we're capable of imagining. One would think that this is a weakness of the theory of possible worlds, but we philosophers are quite confident that further analysis of Aristotle's masterpieces will eventually yield an answer.
Despite the admirable attempts of philosophers to formalize all talk of possibility, the uninformed masses have met this effort with cutting indifference. They proceed to dissect modal claims without using established axioms and helpful abstractions. Such people would have us believe that statements should be interpreted based on context rather than strictly on form and content. Although these interpretations lack the insight and simplicity of Kripke's, their prevalence merits their recognition in this article.
One interpretation is often toted by people who call themselves "common language philosophers". As their name suggests, they prefer to use terms as they appear in their most common forms. These appearances need not occur within highly educated circles, and so common language philosophy mostly employs layman's terms in such a way that nearly anyone can understand. The common language philosophers claim that they see a trend in the usage of "possible"; namely, most people will declare that something is possible if it is conceivable to them. It follows that claims of impossibility are merely ways of expressing that a circumstance is inconceivable and that necessity or certainty are claims that one cannot imagine a given circumstance not existing. Any modal claim, then, is understood to be inseparable from the person making the claim, since conceivability may differ from person to person depending on the knowledge available to said people.
The other major interpretation is the agnostic interpretation. No, I'm not talking about religion, moron. Agnosticism is not a religious movement despite what your Christian buddies might have told you. Agnostics are pseudo-intellectuals who feel they are properly taking mankind's fallibility into account by claiming that we are ignorant of everything but our ignorance. Naturally, possibility as a whole may be rejected as something that would require far more knowledge than we possess in order to be understood. For obvious reasons, this position is rather boring to debate against although it is fun to criticize.
A Solution to Aforementioned Problems
Overpaid statisticians feel they are on the verge of discovering a solution to the general ambiguity of possibility and its numerous philosophical dilemmas. They have compiled data which suggests that the existence of possibility is itself improbable. When they realized that this would be criticized as paradoxical, they dismissed the inconsistency as a result of the inevitable margin of error. Further details are pending.