It gets you through the security line faster.
The following is all it gets you and in my experience also that is all i have gotten over the years.
Exclusive Boarding Lanes at Every Gate
Priority Access lanes are available at American Airlines gates system wide, offering a fast track to board the aircraft.
Customers with Priority Access privileges are among the first to board the plane. Our AAdvantage® Executive Platinum members will board with either First Class or Business Class passengers* followed by our AAdvantage® Platinum and Gold members, and then all other Priority Access customers. Should you arrive at the gate after Priority Access customers have been called, you may bypass the General Boarding lines and enjoy the convenience of boarding anytime via your new dedicated boarding lane.
Simply look for the Priority Access sign in the gate area.