Dynamic microphones work via electromagnetic induction by detecting changes in sound pressure to move a coil of wire in a magnetic field.
When you speak into a dynamic microphone the variations in the air pressure cause a dyaphram which is connected to the coil to move. The difference in voltage at either end of the coild is detected. Dynamic microphones are robust, relatively inexpensive and resistant to moisture. This, coupled with their high gain before feedback makes them ideal for on-stage use.