Explain, expound, explicate, elucidate, interpret, construe are comparable when they mean to make oneself or another understand the meaning of something.
Explain, the most general term, implies a making of something plain or intelligible to someone by whom it was previously not known or clearly understood.
Expound implies careful, elaborate, often learned setting forth of a subject in order to explain it (as in a lecture, a book, or a treatise).
Explicate, a somewhat learned term, adds to expound the idea of development or detailed analysis.
Elucidate implies a throwing light upon something obscure (as a subject, a work, or a passage) especially by clear or luminous exposition or illustration.
Interpret implies the making clear to oneself or to another the meaning of something (as a poem, a dream, an abstraction, or a work in a foreign language) which presents more than intellectual difficulties and requires special knowledge, imagination, or sympathy in the person who would understand it or make it understood.
Construe is preferred to interpret when the difficulties are textual either because of the strangeness of the language (as by being foreign, ancient, dialectal, or technical) or because of ambiguities or equivocations in it. It therefore may suggest either translation involving careful analysis of grammatical structure or a highly individual or particular interpretation.