Podcasting, a term created from two other words (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, and is largely used for audio files.
What is the benefit of podcasting?
Podcasting makes the whole process automatic. You don't have to remember to come by the website and download the latest audio file; iTunes (or whatever podcasting software you choose) does it automatically for you. Then you can listen at your convenience.