Rimming is the act of licking your partner's anus, or having your own anus licked.
Do I recommend it? It isn't really my thing. Like a lot of other people I have issues with putting my mouth that close to anyone's ass, but it's harmless. And when it's done to you, it feels pretty darn good, if kind of tickly. Since I have a policy of not asking for anything I'm not willing to perform, I don't request it of anyone I'm sleeping with. However, I do know several people who are quite enamored of the practice.
There are two things to consider if you're going to try this. The first is cleanliness. This is a great activity after a shower. I know, I know... some people prefer to perform this on a sweaty partner, and that is ok. However, if you're going to try this for the first time, I would initiate it in or after a shower.
The second is disease transmission. Granted, the odds of transmitting something via this practice are relatively small, but humor me. I'd rather take the chances as low as possible, than have you wind up with a nasty infection in either your mouth or your partner's anus that could have been avoided by use of a dental dam. And yes, I know, dental dams are too thick, blah blah blah... Which is why I don't use dental dams. I take a non-lubricated condom, cut the tip off and cut it down one side, and voila! Instant, super-thin dental dam. Condoms are cheaper, too, and easier to find.
So, take a sexy shower with your partner, make a dental dam from a condom (if I can convince you to), and go to town. Have a great time. Remember, as long as the two (or more) of you are having a good time, it's nobody's business but your own.