The question sounds abstract and is not. It asks what your beliefs about the world ultimately rest on, and the two answers lead to strikingly different pictures of how much you can claim to know.
Rationalists take mathematics as the model. Geometrical truths are necessary, certain, and reached by reasoning rather than by measuring things — and if reason can deliver that in one domain, perhaps it can elsewhere. Descartes sought a foundation immune to doubt and built outward from the cogito. Spinoza wrote his ethics in the form of geometrical demonstration. Leibniz argued for innate principles, using the image of a block of marble whose veins already favour one shape: the mind is not blank, but pre-disposed.
Empiricists take natural science as the model, and deny the mind has built-in content. Locke's rejection of innate ideas is the classic statement: if principles were truly innate, children and the unlettered would possess them, and they do not. All materials of reason come from experience, whether sensation or reflection on our own mental operations.
Hume then pushed empiricism to its uncomfortable conclusion, and this is what makes the debate more than a preference. If every idea must trace to an impression, examine the idea of causation: you observe one event following another repeatedly, but you never observe the necessary connection itself. What you have is constant conjunction plus a habit of expectation. The same method dissolves the enduring self — search experience and you find perceptions, never the self having them — and undermines any non-circular justification for induction. Empiricism, followed rigorously, arrives at conclusions its own proponents found unsettling.
Kant said Hume woke him from dogmatic slumber, and his response reframed the question. Both camps had assumed the mind must conform to objects. Suppose instead that objects, as we can experience them, conform to the mind's structure. Then space, time and causation are not features we read off the world nor ideas we invent, but the forms any possible experience must take for creatures like us. This explains how we can have knowledge that is both necessary and about experience — at the cost of restricting it to appearances rather than reality in itself, a limitation his successors spent the following century arguing about.
The labels have since fallen out of use as team names, but the dispute has not gone away. It survives in debates about innate cognitive structure, about whether any knowledge is genuinely a priori, and about how much of what we take ourselves to observe is supplied by the observer — which is the same question the philosophy of science calls theory-ladenness.