Some things you know because you worked them out through pure reasoning, without needing to check anything in the world. Other things you know only because you went and looked — you observed, measured, or experienced something directly. Philosophers call the first kind of knowledge a priori and the second a posteriori, and the distinction isn't just a convenient label for two different study habits. It marks what many philosophers consider a genuinely fundamental difference in how a piece of knowledge can be justified at all.
A priori: justified independent of experience
A priori knowledge is knowledge that can be justified through reason alone, without needing any particular sensory experience of the world to confirm it. That 7 + 5 = 12 is the standard example: you don't need to go count anything to know it's true — pure logical and mathematical reasoning gets you there, and once you understand the concepts involved, the truth follows necessarily. Definitional truths work the same way: "all bachelors are unmarried" is true purely because of what the words mean, not because of any survey of actual bachelors. What makes something a priori isn't that you happened to learn it without any experience whatsoever (you needed some experience just to learn language and mathematical concepts in the first place) — it's that its justification, once you have the concepts, doesn't depend on any specific further observation.
A posteriori: justified only by checking
A posteriori knowledge, by contrast, can only be justified through experience — observation, experiment, or some other direct contact with the world. "Water boils at 100°C at sea level" isn't something reason alone could ever establish; it took actual measurement to discover, and it remains true (or false) based on how the physical world actually behaves, not on the meanings of the words involved. Nearly all scientific knowledge is a posteriori in this sense: however elegant a physical theory's mathematics, its claims about the actual world ultimately have to be checked against observation, because reason alone can't tell you which of several logically consistent physical theories actually describes reality. This is precisely why a priori and a posteriori knowledge require fundamentally different kinds of justification — one lives entirely in the space of logical and conceptual necessity, the other is answerable to how the world actually happens to be.
What we're still unsure about
The basic distinction between a priori and a posteriori justification, and the classic examples used to illustrate it, are standard, well-established territory in epistemology. What remains genuinely contested is whether every truth actually falls cleanly into one category or the other — philosophers including Saul Kripke have argued for cases of necessary truths that seem to require empirical discovery to identify (some claims about identity, for instance), which complicates the assumption that "necessary" and "a priori" always line up neatly, and the exact boundary between the two categories remains an active, unresolved area of philosophical debate rather than a fully settled taxonomy.
This sits inside A Priori vs. A Posteriori Knowledge, one of seven topics in Epistemology, one of five domains in Philosophy, one of seventeen subjects the app can quiz you on.