Moving Coil Microphones, often called dynamic microphones, got their name because they are made with a movable induction coil. This coil is inserted in the magnetic field of a magnet that's is attached to the diaphragm. Moving coil mics do not really do good in captureing transients, but they are the most durable mic out of the three types.
Moving coil microphones are the most durable, as they can also endure the most volume before they start to distort the audio signal. With that said, these microphones are optimal for live use, because they tend not to feedback as easily as the other 2 types. Moving coil mics color the sound more than a condenser mic. The frequencies affected by this coloration are generally between 5kHz and 10kHz. That frequency range is known to add edge, clarity and presence to its sound source, like vocals and guitar. When placed more than a foot away from the sound source, these mics will have a thin sound. with that said, these mics should be used for close mic-ing situations.
Here are some popular moving coil mics Shure SM7, SM57 and SM58 Sennheiser 441 AKG D12, D112, and D1000E Beyer M88
So there is a basic rundown of what a moving coil microphone is. i hope this helps some people out there.