An access control list (ACL), with respect to a computer file system, is a list of permissions attached to an object. An ACL specifies which users or system processes are granted access to objects, as well as what operations are allowed on given objects. Each entry in a typical ACL specifies a subject and an operation. For instance, if a file has an ACL that contains (Alice, delete), this would give Alice permission to delete the file.
To answer your question about "why are they important?" if you do not yet understand, if you do not have them, permissions wouldn't exist. This is how Windows understands who has certain privileges.