RSS (Really Simple Syndication) allows you to get updates from your favorite websites without having to constantly return to that website looking for new updates. Instead, RSS brings the updates to you as soon as we post them.
If you ever decided you are tired of these updates, you can simply unsubscribe on your end and not have to rely on us to remove you from some list like email lists.
A site called Commoncraft created a great video that explains RSS in plain english. It'll probably make more sense than this explanation...
RSS feeds are not easy to read in their standard format so you need a Feed Reader (aka News Reader, RSS Reader, Aggregator, etc.) to collect the RSS feeds and provide the information in them to you in a simple form.
My personal favorite is Google Reader.