Really Simple Syndication (RSS) feeds are a way for websites large and small to distribute their content well beyond just visitors using browsers. Feeds permit subscriptions to regular updates, delivered automatically via a web portal, news reader, or in some cases good old email. Feeds also make it possible for site content to be packaged into "widgets," "gadgets," mobile devices, and other bite-sized technologies that make it possible to display blogs, podcasts, and major news/sports/weather/whatever headlines just about anywhere.
If you want to browse and subscribe to feeds, you have many choices. Today, there are more than 2,000 different feed reading applications, also known as "news aggregators" (for text, mostly) or "podcatchers" (for podcasts). There are even readers that work exclusively on mobile devices.
Some require a small purchase price but are tops for ease-of-use and ship with dozens of feeds pre-loaded so you can explore the feed "universe" right away. Free readers are available as well; a search for "Feed reader" or "Feed aggregator" at popular search sites will yield many results.
A typical interface for a feed reader will display your feeds and the number of new (unread) entries within each of those feeds. You can also organize your feeds into categories and even clip and save your favorite entries (with certain applications).
If you prefer, you can use an online, web-based service to track and manage feeds. Online services give you the advantage of being able to access your feed updates anywhere you can find a web browser. Also, upgrades and new features are added automatically.