RSS or Really Simple Syndication, is a way of reading new content from websites. It allows you to keep informed of the latest developments without the need to constantly revisit a site. Most sites now offer this feature, to find out more have a read of the Wikipedia entry on RSS.
Clicking on a feed should open it in your default feed reader. If you do not have a reader I recommend using Google's online reader to get started. Once you get used to the idea try a software based solution. For Apple users I recommend using Newsfire, or the built in RSS reader in Safari. Windows users try BlogBridge, or RSSOwl.