Can you know something is true without ever checking the world?
Nobody needs a weather report to know that London is either sunny or not sunny today. Whether it actually is sunny, though, requires looking outside. That small gap between knowing by reason and knowing by experience splits knowledge in two, and philosophers have argued over the dividing line for centuries.
The Latin labels mean roughly 'from what comes before' and 'from what comes later'. Knowledge counts as a priori when it can be justified without experience, beyond whatever it takes to grasp the sentence at all. It is a posteriori when it rests on empirical evidence. Mathematics and formal logic lean on the first kind; most sciences depend on the second. If George V reigned at least four days, he reigned more than three, and reason alone settles that. That he ruled from 1910 to 1936 is a historical fact only evidence can establish.
The phrases first turned up in the fourteenth century with the logician Albert of Saxony, who used them for arguments running from causes to effects and back again. Leibniz, Berkeley and the Thomist John Sergeant all worked with the pair, and Plato's theory of recollection in the Meno had already floated the idea of knowledge innate to the mind. Immanuel Kant made it central in the Critique of Pure Reason, arguing that space, time and causality are pure forms the mind brings to experience rather than lessons drawn from it.
In the early twentieth century, logical positivists tried to demystify the whole business. On their analytic explanation, every a priori truth is true by meaning alone, like the claim that bachelors are unmarried, so no mysterious faculty of intuition is needed. Willard Van Orman Quine attacked the foundation, calling the analytic and synthetic boundary an unempirical dogma that nobody had actually managed to draw. His objection badly damaged the positivist project, though whether he was right is still unsettled.
Saul Kripke then pulled apart ideas that had seemed welded together. He argued in 1972 that water being H2O is necessarily true, since identity holds in every possible world, yet it can only be learned by investigation. Most philosophers now treat the a priori question as one about knowing, analyticity as one about language, and necessity as one about how the world must be.
Source: A priori and a posteriori
