Knowledge is the awareness and understanding of particular aspects of reality. It is the clear, lucid information gained through the process of reason applied to reality. The traditional approach is that knowledge requires three necessary and sufficient conditions, so that knowledge can then be defined as "justified true belief":
truth: since false propositions cannot be known - for something to count as knowledge, it must actually be true. As Aristotle famously (but rather confusingly) expressed it: "To say of something which is that it is not, or to say of something which is not that it is, is false. However, to say of something which is that it is, or of something which is not that it is not, is true."
belief: because one cannot know something that one doesn't even believe in, the statement "I know x, but I don't believe that x is true" is contradictory.
justification: as opposed to believing in something purely as a matter of luck.
The most contentious part of all this is the definition of justification, and there are several schools of thought on the subject:
According to Evidentialism, what makes a belief justified in this sense is the possession of evidence - a belief is justified to the extent that it fits a person's evidence.
Different varieties of Reliabilism suggest that either: 1) justification is not necessary for knowledge provided it is a reliably-produced true belief; or 2) justification is required but any reliable cognitive process (e.g. vision) is sufficient justification.
Yet another school, Infallibilism, holds that a belief must not only be true and justified, but that the justification of the belief must necessitate its truth, so that the justification for the belief must be infallible.
Another debate focuses on whether justification is external or internal:
Externalism holds that factors deemed "external" (meaning outside of the psychological states of those who are gaining the knowledge) can be conditions of knowledge, so that if the relevant facts justifying a proposition are external then they are acceptable.
Internalism, on the other hand, claims that all knowledge-yielding conditions are within the psychological states of those who gain knowledge.
As recently as 1963, the American philosopher Edmund Gettier called this traditional theory of knowledge into question by claiming that there are certain circumstances in which one does not have knowledge, even when all of the above conditions are met (his Gettier-cases). For example: Suppose that the clock on campus (which keeps accurate time and is well maintained) stopped working at 11:56pm last night, and has yet to be repaired. On my way to my noon class, exactly twelve hours later, I glance at the clock and form the belief that the time is 11:56. My belief is true, of course, since the time is indeed 11:56. And my belief is justified, as I have no reason to doubt that the clock is working, and I cannot be blamed for basing beliefs about the time on what the clock says. Nonetheless, it seems evident that I do not know that the time is 11:56. After all, if I had walked past the clock a bit earlier or a bit later, I would have ended up with a false belief rather than a true one.