It is very straightforward-
Moving Magnet cartridges produce high voltage, but low current.
Moving coil cartridges produce high current ( higher than MM's ) but very low voltage.
Moving coil step up transformers convert the high current/low voltage of a moving coil to high voltage low current.
Alternately a better option for moving coil cartridges is to use a current gain input stage instead of a voltage gain input stage. This suits the MC better and in theory should have less loss because you are not converting current to voltage as a precursor to the amplification of the very small signal.