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I regularly get the question what “Module” means, regarding gears. Or people just order gears from me, assuming it’s all the same and realise that that isn’t the case. So here is a simple explanation what it is:
The Module is the distance between two teeth measured in millimeters over the circular pitch.
In model trains, most common you experience this:
Older Minitrix: M0.4
Arnold: Both M0.3 and M0.4
You can measure it with a ruler, as the differences are quite obvious, but Fohrmann has a really useful tool for this. More info HERE. It also explains the module system quite obvious.
Image from the Fohrmann website.