I believe my AP Physics teacher in high school was the first person I ever met who used this word regularly.

explicate (ex·pli·cate): / EK spli kayt /
transitive verb

(1) to explain clearly; to interpret or make comprehensible
(2) to develop and explain a theory, hypothesis, or idea and its implications; to analyze and elaborate

[From Latin explicatus, past participle of explicare meaning “to unfold,” from plicare meaning “to fold.”]

Usage: I was awestruck when my father asked if I could explicate the basic concepts of black holes so he could more readily understand them.