Suppose you believe your train leaves at nine, and it does. Do you know it? It depends how you came by the belief. If you checked the timetable, plainly yes. If you guessed, and happened to be right, most people say no — you had a true belief, but you did not know. Epistemology is the attempt to say precisely what the difference is.
The classical answer, traceable to Plato, is that knowledge is justified true belief. You must believe it, it must be true, and you must have adequate grounds. For a long time this looked complete. Then in 1963 Edmund Gettier produced short counterexamples in which all three conditions hold and we still refuse to call it knowledge — cases where a belief is justified and true, but true by luck in a way that bypasses the justification. Sixty years of proposed fourth conditions have not produced consensus, which is itself informative about how slippery the concept is.
Underneath sits the regress problem. Any belief you offer as justification can itself be questioned, and its justification questioned in turn. There are only three ways this can end: an infinite chain, a circle, or a stopping point that is somehow justified without further support. Foundationalists take the third route, holding that some beliefs are basic. Coherentists accept a form of the second, arguing that justification comes from mutual support within a whole system rather than from a foundation. Neither is free of difficulty, which is why the debate is still live.
Then there is scepticism, which is less a position most people hold than a challenge every theory must survive. If you cannot rule out that you are dreaming, or systematically deceived, what entitles you to claim knowledge of the external world? Descartes raised it to defeat it; Hume showed that even induction resists non-circular justification. Contemporary work often shifts from asking whether we can attain certainty to asking what standards actually govern knowledge claims in ordinary contexts — a move that treats the sceptic as changing the subject rather than winning the argument.