Plain English Meaning
A BATD is an FAA-approved desktop or simulator-style training device that lets a pilot practice basic instrument flying procedures on the ground. It doesn't represent a specific aircraft, but it's realistic enough that the FAA allows some training time in it to count toward pilot certificates and instrument currency.
Full Definition
A Basic Aviation Training Device (BATD) is a ground-based flight training device approved by the FAA that provides a training platform for at least the procedural aspects of flight relating to an integrated ground and flight instrument lesson. A BATD must replicate a generic aircraft and meet the requirements outlined in the FAA for ATDs. Time logged in an approved BATD can be credited toward certain and , including instrument currency, within limits set by the FAA.