Both nouns refer to disrespectful or contemptuous words or actions that wound another’s sense of self-worth or pride. Most typically, an insult is a harsh disparaging remark that expresses low regard for someone. Insults are hurled, shouted, or traded like blows. Affront suggests an open show of disrespect towards a person, a group, or a collective value. Your aunt might consider it a personal affront to her that you didn’t let her know you were in the neighborhood, but parked right in front of her house. An affront can offend a specific human attribute (an affront to their dignity or sensibilities), and can be applied to a value (Regulation is an affront to liberty; an affront to democracy or our fundamental rights). Adjectives often paired with affront include serious, blatant, and egregious.
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.
Both these verbs refer to the act of capturing information in writing or other media, with fidelity to objective fact, in order to preserve it. You might record your daily thoughts in a video journal or record lab results in a spreadsheet. Strictly speaking, to chronicle is to record events in chronological order. If you chronicle daily life in the town you live in, you would be recording what you experienced or witnessed daily in a form more like a list than a narrative. These days, the verb is more loosely used—it’s more likely a book or film that chronicles, not a person, and a book that chronicles a journey or history probably wasn’t written as the events occurred, although a blog may have been.