Plain English Meaning
An official FAA sign-off that says a particular ground-based training device is good enough to count for certain pilot training hours and currency, instead of doing all that time in a real airplane.
Full Definition
Formal authorizations issued by the FAA that allow a specific Advanced Aviation Training Device (AATD) to be used for credit toward pilot certification, ratings, and currency requirements as permitted under 14 CFR Part 61. Each approval is granted to a particular device design and specifies what training and experience may be logged in it.
Context Anchor
Seen when an instructor or flight school is deciding whether time in a training device can be used toward a pilot certificate, rating, or required training task.