In its simplest sense, “podcasting” is very much like a subscription to an audio magazine. It’s very different from current Web or radio broadcasts where you, the user, have to “tune in” at a particular time to hear it.
Podcasting, on the other hand, is like TiVo, which allows you to record and save a TV broadcast (in podcasting's case it's audio) for later. In podcasting you can download a recorded broadcast, captured in the form of an mp3 file format, from the Internet and listen to it at your convenience on your computer (using QuickTime, Windows Media, RealPlayer, etc.) or load it to your mp3 device, such as a Rio or an iPod.
With podcasting, you use software to “subscribe” to a service and automatically (or manually) download the newest broadcast once it’s put on the Web.
Here are some links that might help explain more about podcasting:
iPodder definition of podcasting
NPR story on podcasting
USAToday story on podcasting
iPodder resource site
Former MTV VJ Adam Curry’s Daily Source Code site
UPDATE: Here's another link I just found with even MORE links to great info about podcasting.