Epistemology is the study of human knowledge; how we arrive at knowledge, where that knowledge came from, and how we are to trust it (or inversely not trust it). Epistemology is both the most serious philosophical discussion and the biggest joke philosophers love to squabble over. This I will explain, but first let me sketch across the history of this subject.
The question is how do we really know anything? As with most philosophy, most experts will start with the Greeks. The famous painting of the “School of Athens” by Raphael depicts the two teachers (or the teacher and the student who became a teacher in his own rights) Plato and Aristotle in the middle of a group of ancient philosophers, Plato pointing upward, Aristotle downwards. The distinction encapsulated the differences between the two philosophers - Plato and his universal Forms and Aristotle’s down to earth observations.
If you were to put it into a plain metaphor: pretend that the earth and everything physical as far as we humans can ascertain is part of a large cosmic box, and anything outside of it is ethereal or conceptual only. Plato believed the answers had to come from outside of the box, while Aristotle believed we could only come to know what lies outside the box from what is found within the box (the physical world).
Plato believed that when we see red it exists for us to know it because and only because it exists outside of this cosmos in a pure and absolute form or perfect conception, and that goes for all else - round, red, beauty, horse, man, straight, etc. Plato believed that if we could discover and understand these pure Forms, then we would be able to better understand our world. Aristotle was more down to earth. He did not necessarily disregard Plato’s universals, only he declared that the only way we can know anything about anything, including these universals, is by what we know by our five senses.
These two distinctions has split epistemology ever since - it has been known by different names, but the essence of the philosophies have not changed. They are known better today as rationalism and empiricism. Rationalism is knowledge grounded on logic and the mind; empiricism is knowledge produced by the senses. Though I may contend one cannot go without the other -- that sensual experiences without logic to balance it is highly deceiving, and logic without sensual experiences is a mind caught in a fantasy, these two fields of thought have ever been in contention with each other.
More modern concepts have like-wise been devised, but, as most things, they build upon what their predecessors have already devised. The correspondence theory of truth says that something is true if and only if it corresponds to reality. The problem is it begs the trustworthiness of our ability to ascertain true reality. The coherence theory of truth says many different models can be used to find different truths. It is like a puzzle - if it makes sense for something to fit here or there, it probably does, but something can be coherent and yet be wrong, for to be coherent implies knowledge of rationality which is what is being questioned in the first place.
Emmanuel Kant devised a sort of synthesis between rationalism and empiricism where the mind constructs the knowledge that comes in from the senses into what he calls ‘categories’ such as space, time, and causality. While Kant gives a lot of good insight into epistemology, he pulls us no further into knowing what is true knowledge and what knowledge is false.
Then there is the problem of a priori versus a posteriori knowledge. A priori knowledge is the concept of knowledge that is inherently know while a posteriori knowledge is knowledge that is learned. The problem that lies in front of epistemology is, do we trust our a priori knowledge? How can we be certain of it, or even of what is and what is not a priori? What can, should and should not be assumed? Epistemology, the problem before all other problems - how do you know what you know and if you can answer that, how do you know you are correct?