The nerves that transmit signals from one part of your body to another are specialized cells known as neurons. They are similar to the neurons that make up your brain, except that portions of the cells that carry the signals -- the axons -- are much longer. In fact, brains evolved in animals after nerves evolved, so in a way the brain is actually a dense lump of nerve cells.
Nerves are the biological equivalent of telephone lines, carrying signals from place to place in the body. Telephone signals, however, are purely electrical while the signals in your nerves are electrochemical -- that is, they are electrical signals that arise from chemical reactions in the nerves.
Nerve signals in your body may be carried a yard or more along a neuron's axon. The axons of the nerves that control your muscles (motor nerves) and the nerves that transmit senses (sensory nerves) are wrapped in a kind of insulation known as myelin. The myelin coating is not continuous; instead it is broken at various points along the nerves to expose regions called the "nodes of Ranvier." Inside the myelin-wrapped portion of an axon, a nerve signal is primarily electrical, but when a signal reaches a node, it triggers a chemical reaction that boosts the electrical signal, sending a pulse along the axon to the next node. Biologists call the process saltatory conduction, from the Latin word for jump (saltare) because the nerve signal jumps from one node to the next in a rapidly moving electrical pulse.
The conversion from electrochemical signals at the nodes of Ranvier to electrical signals inside the myelin-coated regions speeds up transmission. Typical myelin-covered axons transmit signals at 30-400 feet per second. Axons in your spine and brain lack a myelin coating. Uncoated axons rely on only electrochemical transmission, limiting speeds to about 75 feet per second or less.