What is RSS? (and Atom?)

RSS stands for both Rich Site Summary and Really Simple Syndication but it always refers to the same technology.
It is a mean of transmitting and updating news in an automated way.
Most news sites (including virtually all blogs) will publish what is called an RSS feed which is regularly updated with the latest available headlines and/or articles.
The RSS feed is not human readable. It is an XML format which is designed to be read by machines rather than humans.
Reading RSS
To take advantage of an RSS feed you would use a piece of software called an RSS aggregator. Most of them are very similar to email client programs, but instead of incoming emails, they display news from various sources (from all the feeds you have registered with, or “subscribed to” as is commonly said but it has nothing to do with money). Unread news typically appear in bold, just as unread emails do.
An RSS aggregator makes it very convenient to follow up on news from a large number of sources in a single place. SharpReader is an example of an RSS Reader.
Just like there is webmail, there are also are web-RSS-aggregators. Bloglines is such an online aggregator. Il allows you to track all your news from a single place you can access with a regular web browser.
Also, most modern web browsers will also handle RSS feeds, but in a limited manner. They will use an RSS feed as a dynamic bookmark folder with automatic bookmarks to all the news in the feed. Unlike aggregators, browsers will not save the news if you don’t check on them every day.
Finally, on a more professional level, some websites will aggregate news from different sources onto a single site. Hence the “syndication” in the name.
Producing RSS
While you could theoretically write an RSS file by hand and update it regularly, writing XML manually is a tedious task.
Most RSS feeds are produced automatically by the same content management software which also generates the web pages dynamically. All blog tools for example can generate RSS feeds on the fly. b2evolution is an example of such a blog tool.
Different flavours
There are different versions of RSS in use. RSS 2.0 is the most common. It is used for news/blog feeds as well as for Podcasting.
A newer format, called Atom, is a more standardized way of providing XML content updates. However, it has not gotten wide acceptance yet outside of the blog communities. (Again, almost all blog tools can generate an Atom feed on the fly.)
More info about the history of RSS, RDF & Atom.