Intro text from their site:
... one of the fastest and most exciting ways to navigate the World Wide Web! This completely free service offers easy access to hundreds of thousands of member websites organized by related interests into easy-to-travel Rings.
Webrings were an early means of promoting and indexing sites, prior to the rise of search engines as the defacto portal. They presently do not hold the importance they once did. Now, webring.org has been bought by Yahoo, making the WebRing mechanism less independent than it once was.
The main failing of webrings is that, inevitably, some sites on the ring will either prove ephemeral or will not display the forward link prominently. In the absence of effective forward navigation, webrings degenerate into mere lists of links.
There is another sense of a WebRing that involves dense linking between related sites. Sometimes this just kind of happens because the site operators have similar interests and other times this is explicitly constructed. Of course, this is really a graph and not a ring, but who outside of compsci understands that "graph" doesn't mean a bar chart?
The TourBus system is in some sense a WebRing around Wikis. Unlike most webrings, the TourBus mechanism includes automated ring checking and a certain amount of motivated human supervision to ensure that navigation remains possible.