A priori is a Latin phrase meaning "from the former" or less literally "before experience". In much of the modern Western tradition, the term a priori is considered to mean propositional knowledge that can be had without, or "prior to", experience. It is usually contrasted with a posteriori knowledge meaning "after experience", which requires experience instead of propositions.
For those within the mainstream of the tradition, mathematics, logic and praxeology (the general science of human action, of which economics is the most-widely known branch) are generally considered a priori disciplines. Statements such as "2 + 2 = 4", for example, are considered to be "a priori", because they are thought to come out of reflection alone.
The natural and social sciences are usually considered a posteriori disciplines. Statements like "The sky is usually mostly blue", for instance, might be considered "a posteriori" knowledge.
A priori and a posteriori in terms of constructed languages are specific jargon: the latter means that a conlang is explicitly based in whole or in part upon existing languages (for instance, Esperanto), whereas the former indicates that it is completely invented and based only upon the desires of the creator (for instance, Klingon).
Philosophers have used the term in many different ways.
The use of the term gained foothold through rationalist thinkers like René Descartes and Gottfried Leibniz, who argued that knowledge is gained through reason, not experience. Descartes considered the knowledge of the self, or cogito ergo sum, to be a priori, because he thought that one needn't refer to past experience to consider one's own existence.
Modern use of a priori began with Immanuel Kant who added the distinction between synthetic and analytic truths to the distinction between a priori and a posteriori knowledge.
He argues that propositions known a priori are necessarily true, while propositions known a posteriori are contingent, because a priori knowledge has always been true, according to Kant (e.g. two plus two equals four). A posteriori propositions will depend on external conditions, which may change in time, making the proposition false (e.g. Jean Chrétien is Canada's Prime Minister, which was once true but is now false).
Saul Kripke argues in Naming and Necessity , against Kant, that aprioricity is an epistemological property, and should not be conflated with the separate, metaphysical matter of necessity. In support of this argument he offers several pleas to intuition: "Hesperus is Phosphorus" (the evening star and morning star respectively, both (we now know) names for the planet Venus) necessary if true (see rigid designation), but known a posteriori; while, on the other hand, (of the bar in Paris that formerly served as the standard for the meter), "That bar is one meter long" is contingent (we could have taken another length to define the meter, etc.) but known a priori. That is because one meter is defined as the length of that bar, so the bar must be one meter long - it is a tautology.
Radical empiricists such as John Stuart Mill reject the notion of a priori truths entirely, claiming that all truths come out of experience, and so are a posteriori.
Major contemporary philosophers of a priori thought include Alfred Ayer, Roderick Chisholm and W.V.O. Quine.