A podcast is nothing more than a simple audio subscription. In fact, Wikipedia says:

Podcasting, a portmanteau of Apple's "iPod" and "broadcasting", is a method of publishing files to the Internet, allowing users to subscribe to a feed and receive new files automatically by subscription, usually at no cost. It first became popular in late 2004, used largely for audio files.

There are tons of ways to subscribe to podcasts, and most of them are free. If you use iTunes, the process couldn't be much simpler. To subscribe to Turnip Soup in iTunes, look for the iTunes image on the sidebar and click it! Then, every time we put out a new show, iTunes will automatically download it so that you can listen at your convenience.

If you're really confused, spend a little time on Google; there are lots of people out there ready to help you understand this stuff. Otherwise, enjoy!