A proposition is knowable a priori if it is knowable independently of experience.
A proposition is knowable a posteriori if it is knowable on the basis of experience.
The a priori/a posteriori distinction is epistemological and should not be confused with the metaphysical distinction between the necessary and the contingent or the semantical or logical distinction between the analytic and the synthetic. Two aspects of the a priori/a posteriori distinction require clarification: the conception of experience on which the distinction turns; and the sense in which a priori knowledge is independent of such experience.
a posteriori justification is said to derive from experience and a priori justification to be independent of experience. To further clarify this distinction, more must be said about the relevant sense of “experience”.
There is no widely accepted specific characterization of the kind of experience in question. Philosophers instead have had more to say about how not to characterize it. There is broad agreement, for instance, that experience should not be equated with sensory experience, as this would exclude from the sources of a posteriori justification such things as memory and introspection. (It would also exclude, were they to exist, cognitive phenomena like clairvoyance and mental telepathy.) Such exclusions are problematic because most cases of memorial and introspective justification resemble paradigm cases of sensory justification more than they resemble paradigm cases of a priori justification. It would be a mistake, however, to characterize experience so broadly as to include any kind of conscious mental phenomenon or process; even paradigm cases of a priori justification involve experience in this sense. This is suggested by the notion of rational insight, which many philosophers have given a central role in their accounts of a priori justification. These philosophers describe a priori justification as involving a kind of rational “seeing” or perception of the truth or necessity of a priori claims.
http://www.iep.utm.edu/a/apriori.htm