Sound is essentially energy being transferred through the air. 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. This causes the air to vibrate and bump into the air next to it, which causes the air that is next to it to vibrate...and so on and so on.
Adam Cole, science writer for NPR's Skunk Bear blog, recently explained what sound looks like using Schlieren flow visualization, a method for seeing air distortion from sound waves. As NASA explains, this method of visualization "relies on the the fact that light rays are bent whenever they encounter changes in density of a fluid." In this respect, "Schlieren systems are used to visualize the flow away from the surface of an object."
So while sound itself can't be seen by the naked eye, differences in the air can be. See sound below: