Plain English Meaning
An AATD is a high-end ground trainer that looks and behaves enough like a real aircraft cockpit that the FAA lets pilots count more of their training hours on it toward licenses and ratings than they could on a simpler trainer.
Full Definition
An Advanced Aviation Training Device (AATD) is a ground-based flight training device that meets the FAA's higher-tier qualification standards for Aviation Training Devices, providing a more accurate representation of an aircraft's flight deck, instruments, controls, and flight characteristics than a Basic ATD. Under the appropriate FAA approval (issued via a letter of authorization), an AATD may be used to log a greater portion of training and experience requirements toward and ratings — including — than a BATD permits.