A buttwink is when a person flexes their anal sphincter, causing their anus to visibly contract, effectively "winking" with their asshole. Buttwinking can be performed as an obscene gesture, or in a sexual context it can be either a sign of affection or a greeting.
To buttwink, simply use the same muscles used to defecate to flex your anus.
This act should not be confused with mooning (merely exposing your anus) since buttwinking is considerably more rude.
As Sensei Doug walked to his dojo, the rude employees of a strip mall store lowered their drawers, pointed their behinds towards the window, and contracted their assholes to buttwink at the passing martial artist.
The character Jim Halpert uses from "The Office" to fuck with Dwight Schrute during a customer sensitivity drill over the phone in front of Michael Scott.
Jim Halpert: Hi, This is Bill Buttlicker and I'd like to buy some paper.
Dwight Schrute: Wait, that's not really your name, Bill Buttlicker?
When your "brown eye" (also known as an anus hole) contracts, which causes a closing effct. Once the anus hole opens once more its ends the completion of the "buttwink".
Buttwinks often occur when pinching off a turd while taking a dump or during sexual intercourse (when climaxing for both sexes).
The word that got Peter Griffin into the spelling-bee because his 3rd grade teacher was impressed by the fact he spelt a 3 syllable word even though he didn't do his homework.