RSS is an acronym for Rich Site Summary. It is a format for keeping you updated on all the regularly changing web content on many of the pages that interest you. Blogs, news sites, and other types of online sites inform RSS subscribers of updates to their sites. Here's an excellent video from Common Craft to explain what RSS feeds are and why they are beneficial.
Here's a brief explanation of Google Reader, one of the easiest RSS aggregators to use.
To sign up for Google Reader, just go to http://reader.google.com/. If you already have a Google account, you can use it, but if you don't, it's not a problem. Just sign up with your own email address, choose a password, and you're ready to go. It's as easy as that! The links below give some good tips for getting started and understanding what Google Reader is all about.
How to use Google Reader step by step
Google Reader Help Group (forum)