RSS is a web technology to allow for distribution of regularly published information: web pages, audio/video files, PDFs, etc. The main advantage is that subscribers easily see when new material is posted.
There are many applications, known as aggregators, which will watch an RSS feed and list all the content available from each site. Popular aggregators are NetNewsWire, SharpReader, and Straw. Even modern browsers such as Safari and Firefox can handle RSS feeds (at least to some extent).
The O’Reilly Network has a nice description of RSS.
UPDATE 5/11/18: Some of the above are defunct or the links are bad. Try this list of RSS readers.