Typically, sound waves are mechanical waves. In other words, they are an oscillation (vibration) of matter that transfers energy through a medium. When sound is produced, it is because something is vibrating (like a vocal cord), and this something hits the air next to it in a particular way, which causes all the other air particles to bump together in a particular way, and—Presto!—you have sound.
However, sound can be found as electromagnetic vibrations, as there are electromagnetic waves that pulsate at the same wavelength as the sound waves that we can hear.
But that's kind of another topic (check the link above for more).
Another interesting thing about sound waves is that they can cause pain. Everyone (at least, everyone who has been to a loud concert) probably already knows this. But did you know that you can use sound waves to actually kill someone? Below, the wonderful people over at Power Train Horns have compiled the information you'll need in order to vanquish someone with sound.