The Tallahassee Democrat has a pretty good explanation of RSS feeds.
Basically, if you'd like to retrieve all of the new information that's being published by your favorite websites, RSS or Atom feeds are the way to go. Most sites generate these feeds, so all you have to do is find a way to harness them.
My preferred way is using Google Reader. It's a simple tool that allows you to read all kinds of internet updates in one window. You just sign up (or sign in with your Google Account if you have one) and start adding your favorite sites with the "Add a subscription" button. You can also click on the "Browse for stuff" link on the left, and then on the "Search" tab of that window.
If you use Firefox as your web browser, you can use an add-on called Live Bookmarks to have the information display right from your browser window.
If you use Google Chrome, I'd recommend checking out these extensions to achieve a similar effect to FF's Live Bookmarks:
RSS Live Links
If you use Internet Explorer, I'd say it's about time to start using Firefox.