Hosting
Your podcast episodes are actually digital audio files, usually .mp3, that live somewhere on the web, so people can find and listen to them. A podcast usually combines these files in some sort of serial format, using an RSS feed, so that they can be discovered, downloaded, and listened to in a particular order on mobile devices that do not need internet connection all the time. (The podcast audio files are downloaded, so they do not need the internet to play.)
If you are recording for a class, your professor may indicate what the plan is for hosting. If you are starting your own podcast, you will need to determine how you will host it.
Hosting Services
Libsyn
Podbean
Blubrry
Simple Hosting for Courses
Google Drive