Sound is vibration: back and forth movement. If you touch your throat with your fingers when you speak, you will feel the vibration in your fingers. The speaker phone turns vibration into electricity and then turns that electricity back into vibration. The process is similar to the way a permanent-magnet toy motor that normally consumes electricity to make motion can also be used a generator of electricity if you supply motion. In fact, a speaker is both a motor and generator that vibrates back and forth instead of around and around.
It has everything to do with magnetism, and the magic relationship between magnetism and electricity.
Here is Bruce Yeany's excellent video about how speakers work.
The "Howstuffworks" web site has many good pages about how speakers work.
Here is a great site with cool magnet experiments with the Magnet Man.
Because the speaker actually becomes kind of a generator when it's used as a microphone, consider making this simple electrical generator. One of my students made this. It is so cool to see the bulb light up just by turning the home-made generator.