Welcome to TN!
ctr diff auto = auto locking center differential.
Found this explanation online -
When activated, the center differential locks, resulting in the exact same number of revolutions of the engine being transferred to the back wheels as the front. This does NOT mean that they all turn at the exact same rate, only that the two sets of wheels turn nearly the same number of times. This is because there are still the front and back differentials allowing for small amounts of wheel slip left to right. The final result of this is that if the vehicle is in a situation where traction is uneven or poor (ie. muddy or snowy), no wheel has the potential to spin on its own like in a traditional 2WD setup. All four wheels will turn roughly together, allowing the vehicle to use the wheels that still have traction to move the car while the others do not waste the car's power spinning.