The Nervous System is the communications command and control center of the entire body. It is generally broken up into two categories: the Central Nervous System (CNS) and the Peripheral Nervous System (PNS). The Nervous System is composed of neurons and other specialized cells called glia, that aid in the function of the neurons. 
The Central Nervous System (shown in red to the right) is comprised of the brain and the spinal cord.
The Peripheral Nervous System (shown in blue to the right) is comprised of all the nerves, called axons, that run throughout the rest of the body, which are also connected to the CNS. The main function of the PNS is to connect the CNS to the limbs and organs. The peripheral nervous system is divided into the somatic nervous system, which is responsible for coordinating voluntary body movements, such as those that require conscious control, and the autonomic nervous system, which is responsible for coordinating involuntary functions, such as breathing and digestion.
How The Nervous System Works
In response to stimuli (say someone just threw a hammer at your face), sensory neurons generate and propagate signals to the central nervous system (your body tells your brain that a hammer has just been launched towards your face). The CNS then processes and conducts back signals to the muscles and glands (tells your muscles to make you dodge the hammer). The neurons of the nervous system are interconnected in complex arrangements and use electrochemical signals and neurotransmitters to transmit impulses from one neuron to the next.
Neurons are electrically excitable cells in the nervous system that process and transmit information by chemical signals within the neuron. While variable in size and shape, all neurons have three parts. Dendrites receive information from another cell and transmit the message to the cell body. The cell body, or soma, contains the nucleus, mitochondria and other organelles typical of eukaryotic cells. The axon conducts messages away from the cell body. Sensory neurons respond to touch, sound, light and numerous other stimuli effecting sensory organs and send signals to the spinal cord and brain. Motor neurons receive signals from the brain and spinal cord and cause muscle contractions and affect glands. The junction between two neurons is called a synapse. Chemical synapses allow neurons to form interconnected circuits within the central nervous system. Synapses provide the means through which the nervous system connects to and controls the other systems of the body. The specialized synapse between a motor neuron and a muscle cell is called a neuromuscular junction.
There is a very narrow gap between the neurons called the synaptic cleft. This is where the nerve impulse is transmitted from one neuron to the next. Transmission is done by relaying the message across the synaptic cleft using neurotransmitters, which diffuse across the gap. The neurotransmitters then bind to receptor sites on the neighboring neuron, which in turn produces its own electrical/nerve impulse. This impulse is sent to the next synapse, and the cycle repeats itself.
Neurons are also sometimes classified by the direction in which they conduct nerve impulses. Afferent (sensory) neurons carry impulses to the CNS. Efferent (motor) neurons carry impulses from the CNS.