Prolixity means about the same thing as long-windedness. If someone is yammering on and on and on — that's an example of prolixity. Part of prolixity seems good: we'd all like to be able to put words together easily. On the other hand, none of us want to be boring. That's a major downside to prolixity. Prolixity is similar to "wordiness" — using too many words, or too many long words — when a few would get the job done.