An RSS feed works like this:
Let's say your blog has an RSS feed capability. My blog generates an RSS feed. Ok, now, using your RSS feed capability, you 'subscribe' to my blog's feed.
Now, every time I post something new to my blog and 'feed' it out, your blog will know it. Periodically, your blog will check for these feeds, and a message would pop up on your blog, usually with the title of the latest thing I posted, followed by a brief recognition of who posted it.
This allows you to know when I update my site, without actually visiting my site.
Google's Gmail system allows you to subscribe to RSS feeds, and I subscribe to several this way. It's great for blogs that aren't updated on a consistent schedule. For instance, Tom Ascol's Founder's Blog doesn't update daily. So, since I'm subscribed to their RSS feed, whenever Tom posts something new, I get a link to it from my Gmail page.
It's neat stuff.