This video above shows a transverse wave travelling along a bungee cord. Sound travels in waves too but sound waves are longitudinal waves not transverse waves. This means that the disturbance occurs in the same direction that the wave travels in. See this video below of a slinky which demonstrates a longitudinal wave.

Let us now go back to the example of a drum being hit & try to explain what is happening. When the drum is hit the drum skin vibrates back & forth. (This is represented by the red line in the animation below.) This disturbs the surrounding air molecules. As the drum skin moves outwards it pushes extra air molecules into the space directly ahead of it creating an area of greater atmospheric pressure. This is known as a compression. As the drum skin moves inwards it creates an area with fewer air molecules in it, this is called a rarefaction. These disturbances in the air molecules travel outwards from the sound source as areas of compression & rarefaction - this is a sound wave. Like the Mexican wave, the sound wave that travels is the disturbance - in this case the disturbance from side to side of the air molecules.