Each person's tale could be considered an "event," but here are a few of my favorites:
The Miller's Tale: Here the slightly intoxicated Miller (carpenter) relates a comic tale that is a bawdy parody of the then-popular "high romance" stories. The crux of the tale is that the pretty young wife, Alison, and her would-be lover, Nicholas have concocted a story about another Noah-like flood. They do so to get away from her husband, John, who does fall, literally, for their story. Lesson: Don't be a chump.
The Wife of Bath: An important tale because her story shows how women were essentially trapped by both society & by the Church. The Church insisted that women be married & faithful, but husbands sometimes died, left, & were often unfaithful themselves. Society did not allow a woman to own property or deal in her own money, so women were left with little prospect for survival. The Wife's tale is bawdy but in this light, understandable.
The Pardoner's Tale: Serves as a warning about trust. Though the Pardoner preaches that "the root of evil is greed" he uses the money handed to him in good faith to line his own pockets. It is also instructive about being wary of false gods, as the "preacher" (pardoner) promises that his relics will provide miraculous results. The objects are, of course, powerless.
In these and all of the other tales, Chaucer has a double purpose: to delight, but also to inform.