When your electrical appliances operate, the flowing electricity creates a gathering of electrons which can heat up the appliance's internal parts like the circuit board and wires.
If the electrons cannot escape, this will eventually cause the device to catch fire and possibly explode from excess heat.
The grounding cable prevents this by allowing excess electrons to escape back into the earth, the path of least resistance.
Humans are the same. Every cell in our bodies: brain, heart, organs, skin, bones, etc, all rely on electrical signals to function.