Axons are much like a highly developed dendrite.
The axon carries an electrical signal from the cell body to the synapse. There the signal passes to other neurons or to muscle fibers. The axon may be over a meter long! But in humans, and even longer in bigger animals, like elephants and whales.
The electrical signal of an axon is made by ions that flow in and out of the cell in a chain reaction called an action potential. The speed at which the signal travels depends on how thick the axon is, and how much insulation it has. Insulation is provided by specialized cells called myelin that wrap around the axon.
The axon was discovered by Otto Deiters.