Podcasts are syndicated* channels of programmes, episodes, features or clips that you can listen to on your computer.
You can also download a podcast clip onto your iPod (where the "pod" came from) or other make of MP3 personal music player or mobile phone, and listen to it when it suits you - but less than 1% of non-music podcast clips are actually listened to this way.
Podcast clips are mostly audio. "Vodcasting" was the term originally used for video but it is so ugly everyone has reverted to "podcasting" for both audio and video.
Audio clips are recorded in a computer file format called 'MP3' that achieves high quality sound in a small file size. When you click on a link to an MP3 file your computer automatically downloads and plays it.
The growth in popularity of podcasts has been explosive. The medium has gone from 'nothing' to 'cult' in less than two years. Thousands of individuals and organisations are producing daily and weekly podcasts in the same way that radio stations make radio programmes, and now, so too are the radio stations!
So, from the V&A Museum to the BBC, everybody is producing audio clips for computers and MP3 players.
* Syndication - What does it mean?
One of the reasons podcasting has become so popular so quickly is that you can 'subscribe' to a particlar channel and automatically download the latest clip as soon as it is available.
The podcaster places a file on his website which is a simple list of his episodes written in a standardised code that all computers can recognise and read. Each time he adds a clip or episode he updates this list.
You can use widely available services such as Yahoo, iTunes, or even the 'feed reader' on your browser to monitor any list of podcast clips for the latest episodes. That's called "subscribing".
See the online Wikipedia definition of podcasting for a full explanation... http://en.wikipedia.org/wiki/Podcasting.