Neurons (also called nerve cells) are the basic cells of the nervous systems of metazoan animals, they transmit and process signals. Neurons are located either in the brain, in the spinal cord, or in peripheral ganglia. A neuron is composed of a cell body (soma) and its processes, the axon and dendrite.
A nerve is a group of nerve fibers (axons and dendrites) and it is either for bringing sensory information from skin or organs to the brain (sensory or afferent nerves) or controlling bodily functions by transmitting impulses from the brain to the muscles and glands (motor or efferent nerves). Sensory nerves coming from organs and motor nerves going to glands are also called as autonomic nerves. Sometimes nerves are hooked up to elicit a response on their own, called a reflex, but more often reactions are decided in the brain.
An individual neuron has a sort-of-amoeboid cell body, from which extends a long (potentially several metres) projection called the axon, and numerous shorter protoplasmic branches called dendrites. Nerve cells interact with each other by synapses (or a nerve terminal). A synapse is a junction either between nerves and other tissues (muscle or gland) or between two nerves. Synapses of nerves may be between two axons, two dendrites or an axon and a dendrite. The electrical nerve impulses that are carried throughout the entire length of a nerve are passed to other neurons or organs via synapses by using some specific hormones called neurotransmitters (chemical transmission). Once the message is carried to the other side of the synapse, then it again goes on to be transmitted as an electrical impulse.
Hormones called neurotransmitters are received on the dendrites and affect the voltage of the cell, normally around -50 mV thanks to the ion pump. When it reaches a certain threshold level, there is a dramatic change in the ion pump that causes a electric pulse to travel along the axon. When it reaches the terminals there, it stimulates them to release other neurotransmitters, which are either applied to another neuron or to some kind of muscle.