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Authentication is any process by which you verify that someone is who they claim they are. This usually involves a username and a password, but can include any other method of demonstrating identity, such as a smart card, retina scan, voice recognition, or fingerprints. Authentication is equivalent to showing your government-issued identification (e.g., driver's license, passport) at the ticket counter at the airport.
Authorization is finding out if the person, once identified, is permitted to have the resource. This is usually determined by finding out if that person is a part of a particular group, if that person has paid admission, or has a particular level of security clearance. Authorization is equivalent to checking the guest list at an exclusive party, or checking for your ticket when you go to the opera.
Access control is a much more general way of talking about controlling access to a web resource. Access can be granted or denied based on a wide variety of criteria, such as the network address of the client, the time of day, or the browser which the visitor is using. Access control is analogous to locking the gate at closing time, or only letting people onto the ride who are more than 48 inches tall - it's controlling entrance by some condition that may or may not have anything to do with the attributes of the particular visitor.
Above explanations based on those provided by Apache.org