Microwave ovens are basically lasers-- they use coherent light, which is easier to bring to a much higher power because the amplitudes add coherently. So you can bring power into the circuit and channel it efficiently into the microwaves, getting a more rapid rate of heating.
The microwaves are absorbed in the outer layers of the food-- they get absorbed by water.
They heat the very outer layers, drying them out. At least microwaves can penetrate farther into the food, so the very outside surface eoesn't have to get too hot.

That's my understanding, no doubt there is more to the issue that other responders might bring to bear.