Getting a rim job, but without anal penetration...
Getting your asshole licked, only along the outter ring of the sphinct hole, or "brim" if you will.
The art of licking the outer edge of someones balloon knot.
Sally: "what do you mean you dont like rimjobs?"
Jason: "I guess I just dont want your tongue in my asshole"
Sally: "OK how about a brimjob then?"
Jason: "Mmmmm, Yessiiir!"