Very simply, sound is the vibration of any substance. The substance can be air, water, wood, or any other material, and in fact the only place in which sound cannot travel is a vacuum. When these substances vibrate, or rapidly move back and forth, they produce sound. As described in the How We Perceive Sound: The Ear section, our ears gather these vibrations and allow us to interpret them.
To be a little more accurate in our definition of sound, however, we must realize that the vibrations that produce sound are not the result of an entire volume moving back and forth at once. If that were the case, the entire atmosphere would need to shift for any sound to be made at all! Instead, the vibrations occur among the individual molecules of the substance, and the vibrations move through the substance in sound waves. As sound waves travel through the material, each molecule hits another and returns to its original position. The result is that regions of the medium become alternately more dense, when they are called condensations, and less dense, when they are called rarefactions.
Sound waves are often depicted in graphs like the one below, where the x-axis is time and the y-axis is pressure or the density of the medium through which the sound is traveling.