What is AAA (Authentication, Authorization, and Accounting)?

AAA (Authentication, Authorization, and Accounting) is a model for access control.
Authentication

Authentication is proving who you are.

Authentication answers the question Who is this person?
Authorization

Authorization is defining what you are allowed (and not allowed) to do.

Authorization answers the question What is this person authorized to do?
Accounting

Accounting is keeping track of what you do.

Accounting answers the question What did this person do?