Here is an exerpt from a science book, written for children, on how microwaves work.
"Inside your microwave is a device that sends out microwaves. They are set at a frequency that will affect water and fat molecules. They are the same microwaves we use to send long distance phone calls, satellite TV and radar. The waves change the electrical field and that causes the molecules to flip and spin. When they hit each other, friction causes heat" p. 84.
Church, J. (1993). "You can with beakman: science stuff you can do" Andrews and McMeel: Kansas City, KS.
From my understanding microwaves are safe as long as you aren't the one being microwaved (joke). However, I have heard that, just like some odors can get trapped in plastic, some plastic chemicals can leach into your food. I have to admit that even with this knowledge I still warm some things up in my plastic tupperware.
Hope you find this information helpful.
Keli