Lots of people are still confused about what podcasting is, and why they should care.
Common Craft are always worth a look when you need technologies explaining to you in a simple way, and they've got round to creating a video about using podcasts. While the best way to get your head round it is to subscribe to some podcasts, this video will introduce some of the concepts to you.
Probably the easiest way to get started consuming podcasts is to install iTunes on your computer, and search the podcast area of their store for podcasts on subjects that you are interested in.
Ask your students if they use podcasts. If they do perhaps you can start a podcast on a subject that you are an expert on, and share it with them and other people around the world? Perhaps you can encourage students to create their own as part of their learning.
Just listening to/watching podcasts alone is unlikely to result in deep learning, but it is a way of getting an introduction to subjects and discussions that are going on around subjects. Personally I listen to them while I'm travelling, doing housework, and in other situations where I might be bored and am glad of something to think about. So for me, well made podcasts are a free and welcome way of learning the basics about a subject, without the pain.