This question takes a couple steps to answer.
First, everything is made up of tiny atoms and molecules. The temperature of something is based on how fast itís molecules and atoms are moving around. These molecules are so tiny that we canít see them and when they're moving around, we can't feel them. But when they move around faster, they are hotter.
Next, the microwave works filling the oven with special things called microwaves. The microwave can make certain molecules get warmer be causing them to vibrate faster. Remember that when molecules move faster, theyíre warmer.
Hereís what makes everything fit together. Everything we eat and drink has water in it. It may not seam like there is any water in some thing, but even the air has some water evaporated in it. The microwaves in a microwave oven are exactly the ones needed to make the water heat up. Since food has water in it, it will start to heat up. Thatís how a microwave heats things up.
We have already answered a very similar question. If you want some more details, have a look here
(published on 10/22/2007)