Podcast according to Wikipedia is “a digital media file, or a related collection of such files, which is distributed over the Internet using syndication feeds for playback on portable media players and personal computers. The term, like "radio", can refer either to the content itself or to the method by which it is syndicated; the latter is also termed podcasting. The host or author of a podcast is often called a podcaster."
Though the term "podcast" comes from famous Apple's iPod and broadcast, you don't actually need this Apple gadget to listen to a podcast. You can hear any podcast using virtually all kinds of portable media player.
Here's a video that will help you understand the basics of podcasting.