RSS is a protocol based on XML used for syndicating and aggregating Web content; in fact RSS stands for Really Simple Syndication. In simpler words it is a fast method to get content from different web sources (like news items, blog posts, comments and messages on forums etc) and either read it in a RSS client or directly displaying it onto your own site.
The beauty of it is that you no longer need to go to the site to see if there is anything new there but instead, your software checks it regularly and gives you a message when something new is posted, in a similar manner as your email client tells you when you've got new mails. It's a real time saver for those who try to be informed up-to-date from a lot of different sources.
You get the title and the first few sentences so you can quickly decide if the article is of interest to you and if you want to follow the provided link to read it all.
To subscribe to various feeds you first need to install a reading software but fortunately the possibilities are endless. Even better, popular browsers already have built-in, easy-to-use RSS readers. Here you have a step-by-step guide (with pictures!) on how you can use the Firefox live bookmarks and here is similar guide for Safari.
And here you have a fellow dreamstimer asking you what you have in your RSS feeder. You should answer the man ;)