RSS stands for "Really Simple Syndication" or "Rich Site Summary". It is a way of notifying users of regularly updated content (e.g. news headlines, blog entries, podcasts, table of contents of online publications) on web sites. Typically, an RSS feed contains a list of latest available headlines, summaries of the articles and links pointing back to the full articles. By subscribing to RSS feeds published by your favourite web sites, you can keep track of updates of their contents without the need for visiting the web sites one by one.
You need a software called "feed reader" or "feed aggregator" to regularly and automatically check for new contents in RSS feeds and download them. There are many different RSS readers available. Some are desktop software while some are web-based, many of which are free:
Basically, you subscribe to an RSS feed by entering the feed's URL into the reader. The URL of an RSS feed can be copied when you put your mouse over the "RSS" link or icon, right click, then select in the popped up menu "Copy Shortcut" for IE and "Copy Link Location" for Firefox.
You may refer to the Help page for individual RSS Readers for detailed steps on how to subscribe and view RSS feeds. Here are links to Help pages on using some popular RSS feed readers: