Someone once explained this to me in a very intuitive way. It goes like this:
You’re sitting in the driver’s seat of a car. It is standing still.
You push the gas pedal down 2 cm and hold it there. Your car begins accelerating. That’s the second derivative.
You start pressing your foot further on the gas pedal. Your foot has a velocity on the gas pedal. It is causing your car’s acceleration to grow! That’s jerk.
If you push your foot on the gas pedal faster and faster your foot accelerates on the gas pedal. That contributes to the cars snap.