To enter (a name, etc.) in a register, roll or list
"The registrar asked me to enroll my new student's name on the official attendance list before the first class began."
In plain English: To enroll means to officially sign up for something, like joining a class or becoming part of an organization.
"She decided to enroll in the local swimming class this summer."
The word enroll comes from the Middle French term enrouler, which originally meant to write one's name on a list or register. It entered English via Anglo-Norman and was later reanalyzed as being formed from the prefix "en-" plus "roll."