One user recommended a particular search, and it supplied the following website, which I found very informative. Here is a copy from the first two paragraphs from a transformer manufacturer, Rothwell Audio Products:
“the cartridge operating principle
Moving magnet cartridges, as their name implies, contain magnets which are moved by the stylus’ cantilever, and the movement induces the signal voltage in fixed coils in close proximity to the magnets. In moving coil cartridges the roles are reversed, so now the magnets are fixed and the coils move. The big advantage of moving coils is that the coils are much lighter than the magnets, so they are much more responsive to the motion of the stylus.
The big disadvantage is that the output voltage of moving coil cartridges is about 20dB lower than that of moving magnets, so an extra 20dB of gain is required. The extra gain can be provided by the phonostage amplifier, by an external device called a headamp, or by a transformer. The most commonly found solution is to increase the gain in the phonostage, but step-up transformers are still the best solution where cost is no object.
why use a transformer at all?
It used to be the case that a good signal-to-noise ratio was impossible to achieve from a moving coil cartridge without a step-up transformer. An extra 20 or 30 decibels of gain wasn’t a problem, but doing so with low noise using valves, transistors or op-amps was a problem. Modern transistors and op-amps can now offer much better signal-to-noise ratios but valves still usually need transformers to work successfully with low output moving coil cartridges. An alternative to the step-up transformer is the headamp (or pre-preamp). This is a transistor or op-amp amplifier which raises the output of moving coil cartridges up to moving magnet level. Rothwell offer the Headspace as a high quality, low noise headamp.
Apart from the issue of noise, the sound quality of transformers is something their advocates swear by. The distortion produced by audio transformers is of a completely different nature to that produced by a transistor amplifier. The harmonic distortion in transformers is greatest at the lowest frequencies and falls rapidly as the frequency rises, whereas in transistor amplifiers distortion more usually rises as the frequency rises. More importantly, intermodulation distortion tends to be lower in transformers than it is transistor amplifiers. The outcome is that although transformers aren't absolutely free of distortion (nothing is), the distortion is very benign compared to the distortion produced by many transistor amplifiers. This explains why the sound produced when a moving coil cartridge is used with a good transformer is so sublime and can create an open and spacious soundstage with amazing separation between instruments.
The case against transformers is simply one of cost. Transistors can be as cheap as a few pennies (or less when bought in sufficient quantities) whereas transformers always cost a lot more, by as much as a factor of several thousand, due to the expensive materials used in the core and the cost of the copper windings in terms of both material and labour.”