Rate of Current Change (di/dt)
It is the quantity showing how fast the current changes with time, expressed in amperes/microsecond. It produces a voltage of V = L × di/dt across every inductance in the circuit; a cable inductance of 100 nH and a change of 200 A/µs means a 20 V spike.
Fast switching in the power stage raises the current from zero to tens of amperes within hundreds of nanoseconds. This means a di/dt on the order of hundreds of A/µs. The problem is that no conductor in the circuit is free of inductance: a straight copper track shows approximately 1 µH per metre, while a terminal connection of a few centimetres shows tens of nanohenries.
The voltage that appears across these inductances is imposed directly on the switch. It is therefore not surprising that in a 24 V system the peak voltage you measure rises to 40–60 V; this is also why the MOSFET's breakdown voltage is chosen well above the supply value.
In the field you cannot adjust di/dt directly, but you can reduce its effect: keep the supply and motor cables short, run the outgoing and returning conductors side by side or twisted, keep the terminals tight and place the DC link capacitor close to the driver. All of these reduce the loop inductance and therefore the spike.
The context in which this term is used: DC Motor Driver Selection Guide