what is a podcasting system?

Answer 1

You get to define that. It's whatever you use to create or play a podcast.

Answer 2

A professional podcasting system such as StreamLInk, installs a small internet program that automatically reports to its home web site each day, checks your paid subscription status, and then picks up the new content. Of course it's also possible to just load up some mp3 files on your web site and call that podcasting when someone right-clicks a file name and selects "save target as..."