Why is a diode fitted beween the brushes on a 12 volt DC motor?

The motor is composed of coils. You start with voltage being generated in one direction, which includes a magnetic field around the coil. When the current is interrupted, the magnetic field collapses, and the collapsing magnetic field creates a voltage in the opposite polarity to when the current was flowing. That voltage is not only opposite in polarity; it's also a very High Voltage, which is a recipe for frying any circuitry within the first cycle. However, if you put in that diode to forward-bias consistent with the voltage of the spike, it will divert the power from the circuitry, and also limit the spike to 0.7 volts.