"Podcasting" is a term that actually encompasses a number of different technologies, all working together to deliver audio and/or video content on a particular topic.
A podcast is different from a normal audio file (such as a music file) in that they also allow a user to subscribe to a podcast feed, such that as new podcasts become available, they can be immediately downloaded to your computer for future listening.
I found an extremely comprehensive web site called PoducateMe which will tell you everything you ever wanted to know about podcasting and then some. The author, MIcah Ovadia, even provides detailed technical specifications for an optimal podcasting setup for a mostly reasonable price. If you are interested in creating podcasts, then there is an investment of time and financial resources required to get a podcasting setup that delivers high-quality audio content. Ovadia describes how he set up a podcasting system for about $1000, but you can certainly create podcasts for much less, though the audio quality might suffer a bit. Video podcasts will require some investment in a digital video camera in addition to the audio software and hardware.
Besides the technical aspects of podcasting, Ovadia also explores some applications of podcasting in education and describes the experiences of podcasting at other institutions. Overall, PoducateMe is very, very comprehensive and also a great introduction to the technology. Some of the technical aspects can be a bit overwhelming if you are not an electrical or acoustical engineer, but it the general discussion is still pretty easy to follow.
Podcasts are typically packaged in MP3 format or some other format that maintains a reasonable level of audio quality while at the same time utilizing the minimum amount of storage space. Prior to packaging in MP3 format, an audio file can take up several MB of storage space (over a hundred MB if you include medium-definition or high-definition video).
Podcasts should also be kept relatively short (15-30 minutes). This serves the dual purpose of keeping the files relatively small while also helping to keep a listener’s interest. Many people listen to podcasts in their cars or otherwise engaged in another activity, such as jogging or gardening, so the idea is to give listeners something to focus their minds on while their hands are busy.
Several faculty on this campus are using or have used podcasting technology to supplement their courses and keep students engaged in the materials. I know that the Russian professor (Dr. Irina Ivliyeva) and the French professor (Dr. Audra Merfeld-Langston) have used Audacity in their classes to record their students speaking the foreign languages. The students can then hear themselves speaking and work to correct their pronunciations. As far as I know, these recording are strictly for student use during or outside of class, but Audacity is one of the principle technologies used to create a podcast.
Dr. Richard Hall has used video in his classes to supplement his material as well. He creates some videos on his own, but also uses freely available videos from the web.
If you want to simply use podcasts instead of creating them, then you can subscribe to a number of podcast-hosting services, such as iTunes. One of the advantages of iTunes podcasts is that they have iTunes U. iTunes U is where many universities and colleges post their content, which is freely available for download. MIT is one of several institutions that has a number of courses hosted on iTunes U, so this might be a good way to supplement your courses or spark a discussion among your students.
I think it would be great if we (Missouri S&T) could establish our own presence in iTunes U, but this would require significant time, resources, and investment from all levels of the university. Actually, we should probably start very small, but we would still need some dedicated resources to manage the content and drive the program to make it successful. Stanford University has a PDF document that outlines the steps an institution should take to get started (they were among the first institutions to join Apple in creating iTunes U). Any one interested in getting the ball rolling on this?