Philosophers have distinguished between two kinds of knowledge, a priori and a posteriori.
A priori knowledge is defined as knowledge which is warranted by reference to reason alone, without any reference to any external (to reason) experience at all.
A posteriori knowledge is then defined as all of the other knowledge, which is justified or warranted only after (posterior to) reference to some knowledge derived from sense perception.
One of the fundamental questions in epistemology is whether there are any propositions which we know on entirely a priori grounds. Generally speaking rationalists believe in the possibility of grounding at least some knowledge in the a priori, while empiricists claim that all of our knowledge is ultimately derived from some kind of external experience. The fields of knowledge which seem to rationalists to be a priori knowledge are usually limited to a things like logic and mathematics, which deal primarily with abstract objects, and seem to relate to the external world of objects only in a secondary capacity.
In order to deny that logic and mathematics, constitute real a priori knowledge, empiricists generally claim either that these fields of knowledge can only be derived from experience, as David Hume did, or that they do not constitute "real" knowledge, as Quine did.
Old content moved to /Talk because most of it wasn't about a priori or a posteriori knowlege, but please feel free to move relivant content back here.