From the university of wisconsin – madison:

• Podcasting is a new Internet technology that educators can use to provide students with audio recordings they can listen to anytime, any place – even when they are not connected to a computer.
• The term podcast implies the ability to deliver audio programs like other broadcast media but it has some significant differences and advantages:

• Students can download podcasted audio programs and listen wherever they go, whenever they like;
• New episodes of a podcast are automatically downloaded;
• Instructors can limit the listening audience to students in their course;l
• Instructors can record and publish their own podcasts;
• Podcast production does not require recording studios or professional equipment.

(Thanks Howard!)