When connecting adapter power to a battery powered circuit, reverse current through the battery must be prevented to avoid battery damage.
This can be done with a diode, but that means at least a few hundred mV drop when the battery is powering the circuit, even with a Schottky diode, which wastes power and reduces battery life.
Here's a circuit that uses a MOSFET and comparator to perform that function, so that the forward drop is just the MOSFET on-resistance times the circuit current....