GROUP ON is a database function that allows you to group together a series of results sharing common values for the indicated fields. That allows you to add calculations.
You could for example, count how many students are in Mrs Brown's class, or how many of them had a grade of 80% or more on the last test. Or instantly calculate the class' average for every teacher in the school, maybe grouped by teacher/level, and so on.
Authorization is granting permission for admittance. ACLs provide file system security for protecting files managed by the user. Rule-Based Access Control can be changed by users.