The neuromuscular system has, as its output, motor neuron axon terminals synapsing on muscle cells within a muscle, one axon terminal per muscle cell (although one motor neuron may have hundreds of axon terminals). This is called the nerve-muscle junction. The motor neuron axon terminal releases acetylcholine as the neurotransmitter.
Muscle cells have an excitatory, ionotropic receptor for acetylcholine that opens sodium channels in the muscle cell membrane. These channels also flux a small amount of potassium.
Each action potential reaching a given motor neuron axon terminal releases a packet of acetylcholine that causes an action potential in the muscle cell. This muscle cell action potential has a much longer time course than the one millisecond action potential in most neurons. The effect of the muscle cell action potential is to cause actin and myosin filaments within the muscle cell to slide across each other (mediated by calcium), pulling the ends of the cell together (contracting it longitudinally).
A muscle is a set of chains of these muscle cells. The more each muscle cell is contracted and the more muscle cells in a chain are contracted, the shorter the muscle gets. The more chains that are contracted, the more force the muscle applies. These parameters are controlled by the number of activated motor neurons and the rate of firing in those neurons.