Epistemic luck is having a belief in something for which you have insufficient reason to believe, but for which you are lucky in that your belief does indeed correspond with reality.
Many epistemologists believe epistemic luck is more or less incompatible with knowledge. The purest example of this incompatibility is having no information whatsoever about the probability of a particular event having happened or not, but believing that it did happen. If it so happens that your belief is correct, then this is just epistemic luck and not an indication that you had any real knowledge about the event.
The ubiquity thesis of epistemic luck contends that all of our knowledge of the world that turns out to be true is just epistemic luck since it could always be the case that we have no real knowledge of the world and are brains in a vat, subject to the philosophical evil demon or participating in any number of other skeptical scenarios.
While completely banishing skepticism from epistemology is probably not possible, more pragmatic epistemologists conclude that having epistemic luck is not actually incompatible with true knowledge, often by making the distinction between knowing something and knowing that you know something, and having only that second order knowledge be susceptible to the ubiquity thesis. The argument goes that if you know something of the world, and that something is true of the world, then you have true knowledge, even if you can’t know that you know it, because knowing that you know it involves eliminating all possibility of skeptical scenarios, which you can’t do.