What is a podcast?
"The term "podcasting" is a portmanteau of the words iPod and broadcasting. Although an iPod is currently the playback device of choice for many early adopters of podcasting, a portable music player is not required to take advantage of this method of content distribution. Podcasting is functionally similar to the use of timeshift-capable digital video recorders (DVRs), such as TiVo, which let users record and store television programs for later viewing.

A podcast is much like an audio magazine subscription: a subscriber receives regular audio programs delivered via the internet, and she or he can listen to them at her or his leisure.

Podcasts differ from traditional internet audio in two important ways. In the past, listeners have had to either tune in to web radio on a schedule, or they have had to actively download individual files from webpages. Podcasts are more flexible and much easier to get. They can be listened to at any time because a copy is on the listener's computer or portable music player, and they are automatically delivered to subscribers, so no active downloading is required."

How is podcasting different from streaming audio?
Podcasting is different from broadcasting and webcasting in that it "casts" audio not by a mechanism of centrally pushing audio out to listeners, but by the mechanism of the (distributed) listeners pulling (downloading) the audio files automatically. Podcasters publish (or "podcast") audio files, even in the likeness of radio shows, but it is the individual listener who initiates the "cast" through their subscription and automatic download of the audio program.

Podcasting also utilizes the combination of audio files and RSS to publish descriptive data and metadata associated with the audio. RSS files used in podcasting include dates, titles, descriptions, and links to audio files. These links to audio files within RSS, which are used by podcasting applications, are defined by the enclosure elements in RSS 2.0 and RSS 1.0 (RDF), and all of the original podcasting proper applications were built to work with RSS 2.0.

from Wikipedia