Simply put, RSS stands for Rich Site Summary and Really Simple Syndication. It is a form of web / information feed used to publish frequently updated content such as blog entries, news headlines or podcasts. So for example you will see on the BBC news website that each main section of news - Technology, Scinece, Entertainment etc - all have RSS feeds which you can subscribe to.
Typically an RSS feed will contain a title and summary of the associated website or full text version. The RSS feed allows users to easily keep up to date with websites or news articles that they are interested in.
In order for a user to subscribe to an RSS feed, they will require an RSS reader or "Aggregator". This software makes it easy for a user to subscibe to a feed by simply entering the feed's link into the reader or by clicking an RSS icon in a browser that initiates the subscription process. Much like an email program, the RSS reader will display the feed title and summary text which the user will be able to click on to take them through to the full article on the original website.
Some web browsers such as Firefox have built in rss readers that allow users to subscribe to feeds by simply adding the feed url to a bookmark.
So what makes using RSS so good? Well, as mentioned above, not only do they give your users an easy way to keep up to date with the latest goings on with your business, but it gives them a good reason to keep clicking back to your site and thus help to keep traffic levels high which in turn will help your search engine rankings.