It's just a way of "filing" posts for easier retrieval. So if you want to look at all the posts about tags, search under the tags section on the front forum page ("Browse all tags") and you will see several posts filed under there - including the first two on this thread, as I added in a tag! It would be really useful (if people used it properly) for finding all the threads about a particular book, for example. The size of the tag name in the box shows how "popular" it is - ie the bigger it is, the more posts there are filed under that heading.
More and more websites are using tags now - Amazon have a new tag widget that works in a similar way to show which are the most popular/talked about books on the site.
HTH.