This is different than a rimjob. A rimjob would, however, be a precursor to anilingus. It is the act of plunging one's tongue into the anal cavity of your sexual partner and then swirling and thrusting aforementioned tongue in an effort to make said partner happy.
It is well advised to wash the anus that is to be pleasured thoroughly (and perhaps even douche) before attempting this.
Anilingus is the "scientific" term for applying ones mouth to another ones asshole. Then plunging ones tongue deep within the anal cavity, and swirling it 'round; giving one's partner sexual pleasure.
We're not sure who asked for it, but Brian gave Dana anilingus.
Brian: "Okay, I'm plunging my tongue in now!"
Dana: "OH! Feels good mannnnn!"