Axons are the long, spider-thin, tail-like structures found on neurons (nerve cells). Each neuron has a nerve body, dendrites, and axons, all of which are used to send information throughout your body. The axon carries signals (electric voltages) between the dendrites (the neuron's input sites) and the terminal buttons (the neuron's output sites that are at the very end of the axon).
The signal always travels in the same direction - the signal comes into the neuron through the dendrites, through the cell body (soma), to the axon, and then out the terminal buttons to the dendrites of the next neuron. In this way information travels all around your body by going from neuron to neuron.
You can see an image of an axon (as well as two neurons) by going to: http://www.alleydog.com/images/2neurons.gif