Users subscribe to podcasts using "podcatching" software (also called "aggregator" software) which periodically checks for and downloads new content. It can then sync the content to the user's portable music player, hence the portmanteau of Apple's "iPod" and "broadcasting". Podcasting does not require an iPod; any digital audio player or computer with the appropriate software can play podcasts.
Paul has an nice guide for recording a podcast.

Podcasting differs from broadcasting and webcasting in the way that content is transmitted. Instead of a central audio stream, listeners download audio files remotely and automatically. Podcasts can also include metadata such as dates, titles, and descriptions. Podcasting differs from autocasting in terms of content; podcasts are generally voice broadcasts while autocasting is a speech-synthesized version of regular text blogs. Audioblogs can be easily made into podcasts if they add support for RSS to facilitate automatic retrieval.
To get audio feeds, users simply connect their MP3 player to their computer, go online, and subscribe to feeds they want the podcasting service to provide. Audio content is then pushed from the original source to an aggregator and then to the subscriber. To some, podcasting is one of the most exciting innovations to come along in quite awhile. They see it opening up an endlessly varied universe of audio content to anyone who wants it at any time. Also read Podcasting 101 - Illustrated Tips for Newbie Podcasters