What does closure mean? I am not sure what closure means when used in the context of philosophy. I keep seeing the term closure being used in philosophy, but I have no remote idea of what is meant by that.
In general, to say that a set S is closed under a relation R is to say that if x is a member of S and x stands in relation R to y, then y is also a member of S.
In the case of causal closure, S is the set of physical events, and R is the relation of causation between two events. Causal closure (or at least one version of it) is the claim that the set of physical events is closed under causation; that if a physical event causes some other event, then that other event is physical as well.
In Epistemology there are debates about epistemic closure: whether knowledge is closed under entailment, i.e., if you know p, and p entails q, then you necessarily also know q. Epistemic closure is considered important because it is assumed by many skeptical arguments about knowledge.