To vaunt is to brag and boast and flaunt and go on and on about how great something is. It's over-the-top showing off, and when you exaggerate your greatness, you vaunt to the point of no longer seeming so great.
From the Latin vānitāre — which comes from vānus, meaning "vain" or "empty" — vaunt is a verb for taking praise too far or talking something up too much. Even if it's earned or deserved bragging, vaunting about something gets old and loses it impact. Other times, vaunt, as a noun, is a sure sign that a hard sell is going on — someone is talking big but can't deliver.