The nervous system sending a signal by triggering the action potential of the cell. To trigger the action potential, a certain threshold of membrane potential has to be reached. Acethylcholine is a neurotransmitter that can change the membrane potential, and if the number if enough will trigger an action potential.
If the number of acetylcholine is not enough, there will be no action potential triggered and the signal will not be transmitted. Since the signal won't reach the muscle, then muscle contraction will not happen.
