Rationalism is the early modern position that reason and not sensory experience is the primary source of knowledge: the fundamental structure of reality can be established by deduction from principles the intellect grasps directly, and the senses are an unreliable guide to what is really there.
Descartes gave it its founding method in the Meditations (1641). Doubt everything that can conceivably be doubted, find the one thing that cannot, and rebuild from there. Spinoza took the ambition to its limit, writing the Ethics (1677) in the form of geometrical demonstration and deriving from it a God identical with nature and a determinism without free will. In the Theological-Political Treatise he argued that democracy is the most natural form of government and that freedom of thought cannot be suppressed without destroying the state that attempts it. Leibniz built the most intricate system of the three.
Kant's critical philosophy was a deliberate attempt to end the standoff with empiricism. He conceded that all knowledge begins with experience while denying that it all arises from experience, and argued that the mind supplies the forms within which any experience must fall.
A caution about the word. Political theory uses rationalism in a second and largely unrelated sense, and confusing the two produces avoidable muddle. When Oakeshott attacks rationalism in politics, or Hayek attacks constructivist rationalism, the target is not Descartes's epistemology. It is the conviction that societies can be redesigned from explicit principle by people who believe they have understood them, the position the conservative and Austrian traditions define themselves against. A thoroughgoing epistemological rationalist need hold no such view.