The RSS feed is used by “content aggregators” which display your content without a visitor having to come to your site. These aggregators frequently check if there’s new content available and then display it accordingly. The idea is that you can use a feed reader (the aggregator) to read several different websites, without having to visit each one. Google Reader is one of those, or Flipboard in iPad is another.
In podcasting they use it to display your most recent podcast on a site like iTunes.