Snubber Circuit working
Very simply, the snubber provides a load to dissipate energy from rapid changes in voltage associated with reactive components.  In your diagram, consider what happens when the triac experiences a voltage spike.  The triac itself has capacitance  between the line and the gate, and the spike may provide enough current through this capacitance to turn it "on."

The capacitor provides a high current path through the resistor to ground, preventing the spike voltage from rising quickly and providing a resistive load to dissipate the energy.  At lower frequencies (like the motor frequency) the capacitor impedance is high and the current is low.