Moving Coil cartridges are lighter, more precise, and output at a lower volume. Made with very thin copper wires, the moving coil design allows for a lighter effective tip and more precise tracking than a moving magnet option. The improved tracking allows for a wider range of frequencies; this accuracy and clarity is especially noticeable on the higher end of the spectrum. They are essential components of balanced signal systems.
If you're considering a MC cartridge, you should know: 1) MC cartridges are generally more expensive and are intended for advanced users 2) MC styluses can not be replaced; the whole cartridge needs to be replaced 3) MC cartridges will need a special preamp with MC settings (to account for the cartridge's lower output.)