There are many parts of our bodies which work in a coordinated way when we sing.

When we sing we need to breath, so the air can come out in order to produce the sounds of singing. The organs that help in breathing are the nose, which warms and moistens the air. The nasal cavities are involved in the resonance of tones. We also need the lungs because they control breathing.

In order to sing we also need several muscles, one of which is called the diaphragm. The diaphragm is used to control the outgoing air and the air pressure that goes across the vocal cords which vibrate (and produce sounds) when air is flown over them. Another muscle is the larynx which forms an air passage to the lungs and holds the vocal cords. And finally, we also need the soft palate which is a flexible part toward the back of the roof of the mouth.

From wikipedia I found that many animals like to sing, and there are about 5400 species of animals that are known to sing. Check out that side in order to find more about animals singing.