A zine (pronounced ZEEN) can be many things and can take many forms. Most basically, it is a small-scale, self-published publication, similar to a magazine, which can focus on a variety of topics.
This short video offers a quick and easy background on zines. Added bonus, they interview a zine librarian. Did you know that those even exist?
This video, which is significantly longer, offers a more in-depth exploration of the topic. We get to see zines in a variety of contexts, how some people come together to make them, and how people curate zine collections.
Wikipedia: a small-circulation self-published work of original or appropriated texts and images, usually reproduced via a copy machine
Merriam-Webster: a noncommercial often homemade or online publication usually devoted to specialized and often unconventional subject matter