Zine distros are small distribution organizations (sometimes just a zinester who wants to help others get their zines out there). You can usually buy zines from them online for between $1-$10 each. Timeliness varies from distro to distro - some are small operations which means you can easily get in touch with them but they may need a bit of lead time to get you your zines!
Zine fests are gatherings of many zine creators and distributors. They're a great place to buy zines but also to connect with folks, attend workshops, and share information about your library.
Top image: NYC zine fest, 2016: https://feministzinefestnyc.wordpress.com/category/zinefest/ Photo by Natty Koper.