Really Simple Syndication (RSS) is an XML format for news headlines. With RSS-enabled feeds, other web sites can easily include your content in their sites. And other applications (besides web browsers) can be used to view your content.
Atom is really two different things, both related to syndication (blogs, newsfeeds, and other information which gets updated periodically). The Atom Syndication Format is an IETF standard for publishing entries (single topics or items) and feeds (collections of topics or items). The Atom Publication Protocol (sometimes called the Atom API or abbreviated APP) is a means for finding, listing, adding, editing, and removing content from an Atom repository. While Atom the Syndication Format has gone through the IETF process to become a standard, the standards committee is still at work on Atom the Publishing Protocol, although it seems likely that much of it has stabilized at this point.