"The diode acts as a surge absorber or one way gate. Anytime you turn the power off an inductive load (coil, motor, solenoid, etc) the collapse of the magnetic field creates a voltage spike of opposite polarity to the voltage applied"
Basically it prevents arcing on the key and or toggle switche(s), The inside of the relays use a magnetic field to open the contacts, when turned off, this magnetic fields collapses and creates a massive reverse spike in power (Often many times greater than the forward voltage) The diode is basically a one way valve for power.
If you've ever seen burned or melted contacts on the key or toggle switch, it because a diode wasn't used. The reverse spike can often times fry sensitive equipment.
For the $3.00 it costs to install it's a worthwhile precaution to take