Just noticed no one said this directly: AC can simply and efficiently be converted to a higher or lower voltage through a simple transformer. So in an aircraft, power can be distributed at a relatively high voltage, permitting lighter wiring, and then be converted to a lower voltage (and then to DC) where needed. This is the same reason utilities transmit power over long distances at tens of thousands of volts, covert that to thousands of volts at substations, and then to 120 or 240V at transformers on street corners.
As others have pointed out, its now much easier to convert DC between voltages, but it's still not as simple or efficient as with AC.