Podcasts spun off from the popularity of the iPod. The iPod is a handy way to download, collate and play sound or video files that are available on the internet. Sites that make these available now have a way to tell interested parties (internet users who "subscribe" to the site) when a new file is available. Better than that, the file can be automatically sent ("fed") to a user whenever that user is attached to the internet and activates the appropriate program (an aggregator). Indeed, this program can be neatly embedded in their browser so they don't have to do very muc at all.
The subscription process depends on something called an "RSS feed" which is a button on sites that are able to do this feeding of files to users. Radio stations sometimes do this for their broadcast programs (a kind of listen-again or missed-it service), But, clearly, classrooms could arrange that learners created and published (fed) such material. Here is an explanation of the RSS idea...