A Webring is a group of sites, usually in a similar theme, all linked together in a circle. Each member site puts the special code onto their page.
Webrings don't bring you that much traffic, but they do help a bit. I think one of the one's I'm in (the Page Help Ring) is supposed to bring in about 3-5 extra hits per day. That's not great, but I suppose it's better than nothing. That ring I'm in isn't supposed to be about hits, but about helping webmasters.
There is another concern I've heard brought up. Why link to your competition? You can always think of it the other way, though. They're linking to you too, right?
There are more and more webring services all the time. This is just what happened to Banner Exchanges. One company came up with a good idea, and right away a whole bunch of clones popped up. Some were better than the original, some were not.