Publication lists allow recipients to unsubscribe from different categories of commercial emails. Your newsletters, invites/announcements, and alerts could use different publication lists to let recipients unsubscribe from one and not the others.
If you only use lists or use data extensions without publication lists, an unsubscribe from one message will unsubscribe the recipient from all future commercial emails from your business unit.
Publication lists require you to use data extensions. Take a look at our steps on Switching from lists to data extensions to learn the difference between lists and data extensions, when to use publication lists, and how to start using them.