Here's my explanation...
RSS is a general term for an XML dialect (i.e. a set of rules for how an XML must be formed) that is used for syndication. Actually, there are many RSS dialects (RSS 0.90, RSS 0.91, RSS 0.92, RSS 0.93, RSS 0.94, RSS 1.0 and RSS 2.0) and they are not supported by the same people. RSS 1.0 and RSS 2.0 are competing standards because 1.0 is RDF-based as supported by the RSS Dev Group and 2.0 is UserLand's improvement on 0.94 because they were unhappy with RSS 1.0 path. And to make things even more confusing (yet again), there's another competing standard called Atom. There is lots of debate on comparing RSS 2.0 and Atom 1.0 - read
http://www.intertwingly.net/wiki/pie/Rss20AndAtom10Compared for a sample. OK... but, really, who cares about this except those people that have to choose which dialect to create? And, luckily, almost no one does this by hand because most applications do it for you. Lots of syndicists (is that a word?) even produce two or three formats so they can make everyone happy.
To make it easy, let's just call all these general formats "RSS" and agree it can be thought of as "Really Simple Syndication". But I still haven't said "what" RSS is in a way that is easily understood. So how about an example? Here's a sample of an Atom feed:
<?xml version="1.0" encoding="utf-8"?>
<feed xmlns="http://www.w3.org/2005/Atom">
<title>Example Feed</title>
<subtitle>Insert witty or insightful remark here</subtitle>
<link href="http://example.org/"/>
<updated>2003-12-13T18:30:02Z</updated>
<author>
<name>John Doe</name>
<email>johndoe@example.com</email>
</author>
<id>urn:uuid:60a76c80-d399-11d9-b91C-0003939e0af6</id>
<entry>
<title>Atom-Powered Robots Run Amok</title>
<link href="http://example.org/2003/12/13/atom03"/>
<id>urn:uuid:1225c695-cfb8-4ebb-aaaa-80da344efa6a</id>
<updated>2003-12-13T18:30:02Z</updated>
<summary>Some text.</summary>
</entry>
</feed>
And here's a sample of an RSS feed:
<rss version="0.91">
<channel>
<title>XML.com</title>
<link>http://www.xml.com/</link>
<description>XML.com features a rich mix of information and services for the XML community.</description>
<language>en-us</language>
<item>
<title>Normalizing XML, Part 2</title>
<link>http://www.xml.com/pub/a/2002/12/04/normalizing.html</link>
<description>In this second and final look at applying relational normalization techniques to W3C XML Schema data modeling, Will Provost discusses when not to normalize, the scope of uniqueness and the fourth and fifth normal forms.</description>
</item>
<item>
<title>The .NET Schema Object Model</title>
<link>http://www.xml.com/pub/a/2002/12/04/som.html</link>
<description>Priya Lakshminarayanan describes in detail the use of the .NET Schema Object Model for programmatic manipulation of W3C XML Schemas.</description>
</item>
<item>
<title>SVG's Past and Promising Future</title>
<link>http://www.xml.com/pub/a/2002/12/04/svg.html</link>
<description>In this month's SVG column, Antoine Quint looks back at SVG's journey through 2002 and looks forward to 2003.</description>
</item>
</channel>
</rss>
These are manners of representing written items (or entries) in a way that provides the content, but not presentation. And, to me, this is the fundamental "so what?" answer to why you should care about RSS. Separation of content and presentation allows the consumer (I think of people as "consuming" RSS feeds) to decide how they want to see the information. If you're interested in hearing more about my thoughts on separating content and presentation, let me know and I'll oblige. But in short, I can choose to present the RSS feed in a way that lets we consume hundreds (literally!) of feeds a day in a short amount of time. I could never visit 100 websites a day, that's for sure. As I'm consuming these feeds, I might choose to present some classes (i.e. forum extracts) different from others (i.e. news items).
Anyway... back to RSS. What you don't see in the above samples is something that RSS does that relates directly to us MC users: enclosures! Enclosures - as in a link to some other file. RSS 2.0 allows a single enclosure (there is an <enclosure> element) whereas Atom 1.0 allows multiple enclosures (via <link> elements). These enclosures can be anything, but practically they are almost always audio files (MP3s) and when they're used the RSS feed is considered a "podcast".
The biggest shortfall from my perspective is that there's no way to relate RSS items hierachically. So it can't replace things like NNTP and it's a bit of a kludge for reading forums. I'm not sure this will ever be addressed, because most things published as RSS don't care about hierarchy.
RSS aggregators (I don't like the term "RSS readers") collect these RSS feeds and organize them in a way that lets you tell which items you've already seen. Remember, a single RSS feed can have hundreds of items in it and you have to have some way of keeping track of which ones you've read. I'm a great fan of FeedDemon (Nick Bradbury is the best software creator I've ever known!) even though it's gone the way of a subscription model. Take a look at
http://www.bradsoft.com/feeddemon/screenshots/ for some screenshots.
I'm sorry I didn't have time to make this post shorter...