What is a clincher browband?

It sounds like some kind of horrible torture tack, but it isn't. It's a browband that has metal studs or beads on the front - they're either brass or silver colored. The backing is thick leather, so the studs aren't noticed at all by the horse. It's entirely for looks and is commonly seen in dressage, including the dressage phase of eventing, or on in-hand bridles used when showing stallions. The color of the leather (black or brown) and metal is chosen to complement the horse.

So, it's just horse bling.