If you click on one of the Podcast links, a file will be returned in a format that a "Podcast Feed Reader" recognizes. A "Podcast Feed Reader" can be a special software on a PC, or a mobile devise like the Apple iPod, or a MP3 player. Again when you click on one of the Podcast links (under "Subscribe to a Podcast") a feed file will be generated. But the most important thing to pay attention to is the URL in your browser that is shown at the top - that will look something like the following:
http://www.media.churchofgodcarmichael.org/gospel-music-podcast.feed?type=rss
The way you subscribe to the podcast is by copying that full URL into your "Podcast Feed Reader". Then when new sound files are published under that particular podcast, your "Podcast Feed Reader" will automatically pick it up for you, according to how you have configured your "Podcast Feed Reader" (and how connected it is to the Internet).
For more information on podcasting you can go to the Wikipedia article on "Podcasting".
