There's a definition of push technology on Wikipedia, but I don't think this definition will clarify matters much :-)
The important concept here is that you somehow subscribe to a source of data (in this case, you subscribe to a podcast through software such as iTunes), and when this source has some new data, the source will broadcast it and your software will catch it (again in this case, this means that iTunes will download the new episodes of the podcast).
So instead of you going to the source to check for new stuff, the source pushes the new stuff to you.
It's like eating at Grandma's house. She keeps putting food on your plate.
This point about push technology is the defining point. We already said that you don't need the pod of podcasts. Without some kind of subscription available, there's no cast to the podcast. If the source isn't nudging the new episodes at subscribers, it's just a bunch of audio files on the Internet. Not that there's anything wrong with that.