Plain English Meaning
ANDS is a quick way to remember that speeding up makes the compass swing toward north, and slowing down makes it swing toward south, when you are flying east or west. The compass is wrong for a moment, not the airplane.
Full Definition
A memory aid used in northern hemisphere flying to recall how a magnetic compass behaves during changes in airspeed on an east or west heading. When the aircraft accelerates while heading east or west, the compass momentarily indicates a turn toward the north. When it decelerates, the compass indicates a turn toward the south. The actual heading has not changed; only the compass reading is temporarily in error.
Context Anchor
Used in flight training when learning magnetic compass errors, especially during instrument training and basic attitude instrument flying.