While the AC supply is present, D1 has +15 volts on its anode, and is forward biased.
Since there is 0.6 volts across the diode, there is +14.4 volts on its cathode.
This voltage powers the equipment.
D2 is reverse biased since its anode is less positive than its cathode.
D2 is non conducting and the battery is isolated.

If the supply fails then the +15 volts disappears, and D2 becomes forward biased and conducts, to power the equipment.

The diodes STEER the voltages.