With so many advances and developments in computer and internet technology, it is sometimes difficult to predict which ones are just flashes in the pan and which will stick. Podcasts seem to be in the latter category.
A podcast, basically, is a media file (usually audio) that is distributed over the internet for download to computers and personal listening devices. The files are "broadcast" online through a subscription feed such as RSS (Rich Site Summary), which facilitates syndication and also allows a website's frequent readers and listeners to track updates.
Since the inception of podcasts in 2003, the world of podcasting has exploded. Within just a few months of the first podcasts, literally thousands were available. This is the beauty of the podcast: as long as one has a microphone and the right software, anybody can create a show. Usually a podcast features one type of 'show', with new episodes released either sporadically or at planned intervals such as daily or weekly. In addition, there are podcast networks that feature multiple shows on the same feed.
The name "podcast" is a portmanteau, a combination of the words "iPod" (a personal, portable MP3 player put out by Apple) and "broadcast." Of course, one does not need an iPod to listen to a podcast, and for this reason, there has been an after-the-fact suggestion that the "pod" stands for "Personal On Demand."
Many radio stations, such as NPR affiliates, offer podcast versions of their regular series. And this might be the easiest way to think of a podcast: as the web's answer to a television or radio series.
More information on portable audio