Really Simple Syndication or RSS as it is called is a web feed format which lets you read news, blogs, articles, listen to audio and watch videos without the need to visit the particular site which hosts the content.
RSS, sometimes also referred to as "Rich Site Summary" has revolutionized the way information is consumed over the world wide web in the last few years. Though it is yet to go mainstream, it is used by a huge number of people around the world who spent a majority of their 24 hours on the internet.
For a website to let its readers read its content via RSS, it would need to burn a feed using a service such as Feedburner or any other similar service. Once the feed is created, the website owner could have a nice RSS icon displayed on his site like the one you see in the picture above.
Visitors who wish to subscribe to the site can click on the RSS icon and subscribe it via a feed reader. There are number of both desktop and browser based feed readers available. The most popular among the desktop tools is FeedDemon and the one which dominates web feed reading space is Google Reader.
Check out this amazing video by Common Craft which explains RSS in plain English.