Both words refer to making an idea or thing clear or comprehensible. Explain emphasizes the act of giving a complete account of something. After a teacher explains a concept, she might then quiz students to see how much they have understood. Whereas you can explain something badly and then try to explain more fully or in more detail, elucidate implies that clarity is accomplished (whether or not the reader or listener is able to see it). Elucidate refers to making something clear or more clear for others, as if shining a light on or through it—a speaker, a book, a series of studies, or research results are typical subjects of elucidate. Typical objects include a mechanism, relationship, role, or structure—concepts or processes more complex, perhaps, than those that can be exhaustively explained.