Plain English Meaning
Official FAA sign-off that a particular ground-based training device meets the standard to count as a Basic ATD, so time spent training in it can be logged toward certain pilot certificates and currency requirements.
Full Definition
An FAA letter of authorization issued to the manufacturer of an Aviation Training Device (ATD) certifying that the device meets the requirements for use as a Basic Aviation Training Device (BATD). The approval permits the device to be used for logging a limited amount of training and experience toward pilot certification and recency, as set out in 14 CFR Part 61. The approval applies to the device itself, not to any individual operator or training program.