Well, I also just learned the word (from you!). You shouldn't worry about that word ever coming up since I as a native speaker have never used it or seen it (maybe if you're in a spelling quiz??). As I see now it's an adjective describing someone to be like Don Quixote, and therefore possibly visionary, chivalrous, or rashly unpredictable. An example would be, Romeo was quite quixotic toward Juliet, the love of his life.

Example sentence: "Wouldn't you say that Bob's mission to expose government cover-ups of Mind-Control experiments is rather Quixotic"? (Pronounced: kee-oh-tik, I believe). Don Quixote, if I have heard correctly (never having read the book myself), was a self proclaimed knight who sought to defeat the "giants" (which were really Windmills). On a horse with a lance as his weapon, this would have been an utterly futile quest for many reasons. When someone says that something or another is Quixotic, they are likening it to Don Quixote's quest. (Now, it is entirely possible that I am off on a few details here. If someone knows better, please correct me).