Anonymous credential systems are a means for authentication, i.e. a way to implement access control.
Currently authentication is mostly identity-based, i.e. in order to gain access to something, you tend to tell the access control mechanism exactly who you are. For example, on the internet, you typically authenticate with your email address and a password. When going to see an age-restricted movie, you present your passport to the cinema.
The issue is that during these processes, the user leaks a lot more information about their identity then perhaps necessary. For example, the cinema does not only learn that you are at least 18 years old from your passport, but also your full name, address, nationality, and your exact birth date.
Anonymous credentials provide a solution to that: they enable authentication without identification, i.e., you can prove some statement about yourself (e.g., that you are at least 18 years old, or that you have access rights to some resource), without revealing any other information about you. Like a passport, an anonymous credential encodes a list of authenticated attributes, e.g., name, address, nationality, birth date.