It damps oscillations, and therefore is stabilizes the steering parts. "Dampener" is like "inflammable": unnecessary syllables, but not wrong.
My Mille didn't come with one, and the steering has been stable up to the bike's top speed, but I'm still considering adding one. With any motorcycle, when something goes wrong, like you hit an oily spot in the road while leaned over, a tank slapper can get started, and a damper can keep things stable.