Sound propagates as a longitudinal wave. Although air is relatively light, it does weigh something. Air is also "elastic": if you try to compress it, it will push back. Given that air has both elasticity and mass, you can imagine the air around you as being made up of little "lumps of air", where each lump is connected to the next lump by an elastic spring.
If an object (e.g. the small bar at the left edge of the animation below) pushes against such a column of air, it compresses the air immediately next to it. This compression propagates away from the object as a "compression wave", as each lump of air pushes against its next neighbor. If the object then returns to its original position, it draws the air back, creating a "rarefaction wave" which follows the compression wave.
The animation here, essentially an animated version of Figure 1.17 of "Auditory Neuroscience", illustrates this.