Most professional microphones pick up sound waves and convert those waves into an electrical signal to be used by audio equipment in one of two ways.
A dynamic (or moving coil) microphone operates by using a wire coil and a magnet to create the audio signal. The interaction of the wire coil and magnet is called electromagnetic induction and is responsible for generating an output signal voltage. A diaphragm is attached to the coil, and is mounted within the mic so that it can move in response to a sound wave. When the diaphragm vibrates, the attached coil moves back and forth within the magnetic field. This motion within the field generates an electric current (induction), which can be converted by audio equipment into sound waves. The strength of the electrical current is directly related to the motion of the coil.
Dynamic mics are great general-purpose microphones. They have less moving parts than condenser mics, and as a result they're typically more rugged and durable. In addition, since they generate their own current, no external power source is required.
The physics behind the moving coil can contribute to limitations in frequency response. Generally speaking, dynamic microphones are less sensitive than condenser mics.
In a condenser microphone a voltage charge is applied to the diaphragm by either a battery or phantom power. The diaphragm is mounted very close to a stationary back plate. Sound waves hitting the diaphragm causes it to move closer and farther away from the back plate which causes electrical charge fluctuations to occur. The interaction between the diaphragm and back plate creates an electrical component called a capacitor (or condenser), and the resulting variations in voltage can be reinterpreted as sound waves by the receiving audio equipment.
Condenser microphones are very responsive and create a much stronger signal than dynamic mics. This makes them an ideal choice for professional settings such as studio work, where it's important to pick up vocal subtleties.
Typically condenser mics have more moving parts than their dynamic counterparts and are less durable. Also, since they do not generate their own current they require an external power supply. (Battery or phantom power)
What is phantom power? Phantom power is a direct current (typically between 12 and 48 volts) that supplies microphones with power through audio cables. 48 volt phantom power is the most common and is often supplied by microphone preamps and audio mixers.