What is the purpose of connecting Zener diodes between a MOSFET gate and its source or drain?
Why A MOSFET gate is separated from the channel by an extremely thin silicon dioxide insulator, and that layer can be punctured by only a few tens of volts. Since the gate draws essentially no current, even the small charge from handling or a nearby static discharge can build up enough voltage to destroy it. Back-to-back Zener diodes built in from gate to source (or drain) conduct once the voltage reaches their breakdown value, clamping the gate at a safe level and bleeding the static charge away. The tradeoff is a small amount of added leakage and input capacitance, which is why some RF MOSFETs omit them.
Watch out The choice about keeping gate voltage in spec to prevent overheating is close but misses the point: the failure mode being prevented is instantaneous dielectric puncture of the gate oxide, not thermal runaway. The reverse-bias voltage reference idea describes how a Zener is used in a regulator, not here.
Thin gate oxide plus static equals dead FET. Internal Zeners are the MOSFET's lightning arrestor.