Why do aircraft use 400 Hz AC instead of the 50 or 60 Hz of wall outlets?
Induction motors turn at a speed proportional to frequency, so a high frequency power supply allows more power to be obtained for the same motor volume and mass. Transformers and motors for 400 Hz are much smaller and lighter than at 50 or 60 Hz, which is an advantage in aircraft (and ships). Transformers can be made smaller because the magnetic core can be much smaller for the same power level.  Thus, a United States military standard MIL-STD-704 exists for aircraft use of 400 Hz power.

So why not use 400 Hz everywhere? Such high frequencies cannot be economically transmitted long distances, since the increased frequency greatly increases series impedance due to the inductance of transmission lines, making power transmission difficult. Consequently, 400 Hz power systems are usually confined to a building or vehicle.

Source

Further discussion of aircraft electrical systems

Further, further discussion of aircraft electrical systems

Added: cool discussion of the use of 400hz with Cray supercomputers on another S.E. forum