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Epistemology is the analysis of the nature of knowledge, how we know, what we can and cannot know, and how we can know that there are things we know we cannot know. In other words it is the academic term associated with study of how we conclude that certain things are true.
The subject of Epistemology is incorporated into the International Baccalaureate program, in the Theory Of Knowledge subject.
Traditional View of Knowledge
Philisophical tradition going back as far as Plato characterises a proposition as known where it is, at a minimum:
2) That belief is "justified" and
3) it is true.
Most modern epistemology concerns itself with two problems, the adequacy of that definition and analysis of what it means for a belief to be "justified".
Is the "traditional view" adequate?
In his essay Is Justified, True Belief Knowledge? Edmund Gettier gave a number of examples where the traditional view appeared to be insufficient to establish a proposition as known. That is to say the examples were of beliefs that where both true and justified, but do not appear to have been "known", usually because they are "accidentally true". Solutions to the "Gettier Problem" centre around ensuring that there is a direct connection between justification and truth.
What does it mean for a belief to be "justified"?
Whilst it is, almost, universally held that if a proposition is known then it is true the reverse is not the case. If you flip a coin and correctly call "heads" you speak the truth but you did not know, you guessed. To be known there must be something more than true belief, this is what is meant by "justification".
Several theories, and controversies, about justification have arisen.
Reliabalists hold that a belief is justified if it has been arrived at by a reliable process. For example you might look at a reliable clock and come to believe that it is now 2:00 pm. Provided it is 2:00 pm (i.e. that the proposition is true) and that the clock is reliable then a reliabalist would hold that you know that it is 2:00 pm.
Internalism and Externalism
An "internalist" holds that the justification for a proposition is internal to the subject believing it, for example his or her mental state. An "externalist" holds that the justification for a proposition is external to the subject believing it, for example the reports of others.
Skepticism, the belief that nothing is known, has been a key methodological assumption of epistemologists since Descartes. In order to demonstrate knowledge the epistemologist imagines the best arguments a skeptic could muster and tries to refute them.
Whilst skepticism is normally a methodological conceit some philosopher do subscribe to a skeptical position.