'Epistemic closure' is one of those terms that has come to have two inconsistent meanings, a technical one and a popular one. The technical meaning is that you are operating in a system in which, if something is known, and that something entails something else, then that something else is known. That is, if I know that the sky is blue, and if the sky can't be blue unless it exists, than I also know (simply because of these two things) that the sky exists; epistemic closure would apply if all known truths were like this -- we would then say that knowledge is closed under entailment. You could have variations on this. although entailment is the most common one; for instance, one could have an epistemic closure principle in which knowledge is closed only under equivalence, in which case we'd have to talk about equivalence rather than entailment. But the basic structure is pretty straightforward. Closure occurs when a property that applies to something also applies to everything you can get as a result by a particular operation; and epistemic, of course, just means 'having to do with knowledge in some way'. The concept is useful because it raises all sorts of philosophical questions.
In the past few years, though, the phrase has taken on a popular use. If Wikipedia is to be trusted, we owe Julian Sanchez this obfuscatory usage. In this usage, it just means 'closedmindedness'. There is absolutely nothing lost by using the phrase 'closedmindedness', except that everyone knows what that means; and there is absolutely nothing gained by using 'epistemic closure' except that you might more easily get the insult by the slow-witted. The term arose in the context of politics, and it touched off a pretty big bunch of posts and discussions, mostly of the uselessly handwringing or idiotically supercilious kind in which people speculate airily about the characters of others without any serious evidential basis, but I've noticed it a few times here and there, so perhaps it is coming back. If you mean that someone has a closed mind, though, just say that they have a closed mind; 'epistemic closure' makes you sound either pompous or cowardly or both.