RSS (Really Simple Syndication, depending on who you ask) allows certain web browsers and specialized programs to automatically check for updates to a page.
To enable RSS as administrator, go to Configuration and under Variables: Miscellaneous set enablerssfeeds to Yes. Then in Configuration: Modules you can enable an RSS feed for each module. Finally, in the settings for each individual instance of a particular module you must enable the RSS feed and specify the settings (e.g. how many articles to display, what kind of article).
To subscribe to an RSS feed from moodle, click on the orange 'RSS' button and copy the address from your browser bar to your RSS reader software. Although most web browsers will automatically detect an RSS feed (IE7 and Firefox), moodle does not seem to be sending them the correct information (as of 1.5 - is this fixed in 1.6?)