
Web feeds (RSS feeds, Atom feeds, webfeeds, or just feeds) make it easy to keep up with websites you'd like to keep track of, without visiting each one to see if anything is new. Feeds bring changes from your favorite sites to one central spot.
Web feeds work somewhat like newsletters, but they're a better solution. You "subscribe" to a newsletter by giving your email address to a mailing list. In contrast, you "subscribe" to a web feed by adding the feed's address to your feed reader. That creates a "pull", not a "push" connection. The sites you subscribe to know nothing about you, and you can easily unsubscribe at any time.
Most blogs and other dynamic websites — those that add fresh content regularly — have web feeds. Baseball related blogs and news sites make good examples. There's always something new, even during the off season. If you're a baseball fan, you'd probably want to follow at least a few of them. You could easily follow a dozen if you wanted to.
Your feed reader periodically checks each feed for the blogs or websites you're following to see what, if anything, is new. If a result looks interesting, you can click a link that takes you to the rest of the content.
It's not easy to explain just how feeds work with simple prose. You'll catch on quicker by just trying a few of them. ;-)
Original Signal is an all-on-one-page feed reader. There are various topic pages there -- buzz, jobs, tech, digg, gadgets, etc. You may not be interested in those specific topics but you'll get a feel for feeds there.
You can find webfeeds for virtually any topic -- sports, digital photos Edinburgh, world news, movie reviews, Microsoft, the blues -- anything that strikes your fancy.
A few more examples: Robert Scoble is a prolific, entertaining geek-blogger. Thomas Hawk's photos on the Flickr photo blogging site. Jim McLennan's blog on the Arizona Diamondbacks. The Google blog.
Sometimes you'll see "RSS 0.9", "RSS 2.0" or "Atom" links. Most feed readers can use any of them. (I'd pick Atom or RSS 2.0.) Some readers can only use one of the formats. Pick the one that works for you.
Other ways to subscribe to web feeds