Ring signatures mean that when you sign a tranaction to spend an output (coins), no one looking at the block chain can tell whether you signed it or one of the other outputs you choose to mix in with yours. With a mixing factor of 5 or 10 after several transactions there are millions of possible coins all mixed together. You get "anonymity" and mixing without having to use a third party mixer.

There are a number of other anonymity features, explained in the first post on this thread and the pages linked from there.