Well, you noticed how the inner walls of the microwave are made out of metal, right? The microwave is named that because it utilises microwaves. It's called dielectric heating. It passes waves of non-ionizing microwave radiation through the food and heats it through the friction. Because microwaves can't pass through metal, they're reflected off each wall.

You noticed how the food rotates, right? By agitating the oscillating molecules of the microwaves, the kinetic energy of the food is amplified, resulting in it being heated essentially by itself - with a little help.