To understand rss you have to understand xml. XML is a file format for data exchange that uses tags in the same way that html does. I can't go much further in this complicated subject without writing a dissertation on xml, and I'm not going to do that. Suffice it to say that when you look at an xml file, it tends to be pretty easy to understand the format. For example you might see something like this:
Fred
Smith
Bob
Jones
RSS is a specification for a type of xml file that deals with syndicating news stories. Take a look at yahoo as an example and some of their rss feeds, as an example. In general you have a title, an author, the date of the story, an abstract, and some other assorted information, along with a link back to the site where the full story can be accesssed.
Once sites started providing rss feeds, it became easy for aggregation sites to bring a variety of rss feeds together, and also for people to use them to allow for rss reader applications.
In practical use, let's say you have a blog with stories you write and publish, and your site offers the rss file to summarize your stories. This rss feed only changes every so often (perhaps it will be updated once an hour or once a day).
Sites or readers will read in your rss feed, and will know not to come back to your site to get new stories until the period has passed, thus minimizing the need for people to chew up bandwidth to your site only to find that you have not posted any new stories.
In summary, rss feeds can be used to provide a quick list of content in a standard way, so that other sites can feature links to your content in an automated way. Because .rss is a standard, any program that can parse the rss file can make use of it, perhaps to provide a searchable index, or to allow people to have aggregated pages of information pertaining to topics they are interested in.
People have found interesting ways to make use of this simple concept... one of the best known examples being podcasts, which use the rss format to provide the links that Itunes uses pull the audio files down off the internet and into your itunes library.