Kant on the distinction between a priori and a posteriori
Kant's clearest formulation of the a priori/a posteriori distinction is found in the following passage:
We shall understand by a priori knowledge, not knowledge independent of this or that experience, but knowledge absolutely independent of all experience. Opposed to it is empirical knowledge, which is knowledge possible only a posteriori, that is, through experience. (Critique of Pure Reason, B2).
This formulation is clear, but still problematic. Kant presents us with a simple either/or. Either a statement can be known absolutely independent of experience or a statement cannot be known absolutely independent of all experience. The apriority of any statement then depends upon whether or not the statement can be known absolutely independent of experience, which is different from whether or not the statement is known absolutely independent of experience. For example, assume, as Kant holds, that "Every alteration must have a cause" is an a priori statement. It is still possible to know this statement a posteriori. For example, perhaps this statement is known by an appeal to authority; many propositions of mathematics are known this way if we accept that a calculator is an authority on mathematics. Or, perhaps causality is known psycho-socially (as Hume might have).
Kant's distinction between a priori knowledge and a posteriori knowledge is clear and straightforward -- a statement P is either n or it is not-n. Difficulties with this distinction arise, however, in the application of these terms to actual statements (as one can see if they ever sit on in an Intro to Philosophy course). It is not always clear if a statement can be known without experience, especially if the statement in question is already known through experience or speculated to be known through custom or some other psycho-social means.