To boggle is to amaze, astonish, or overwhelm. Your mind might boggle at all the information your physics teacher writes on the board on the first day of class.
You'll most likely find this verb in sentences like "My brain boggles at the outfit she decided to wear to the party," or "When you watch this movie, your mind will boggle at the special effects." Along with the even more common adjective mind-boggling, boggle comes from the Middle English bugge, or "specter." Boggle originally meant "spook," or "start with fright."