Sound is defined by three types of waves; mechanical, longitudinal, and pressure waves.
In general waves can be described as a disturbance that travels through a medium. For sound to be described as a mechanical wave it must travel through a medium, such as air or a liquid. Secondly it must have a source. For example when you hear a car horn the source of the noise is the horn in someone's car. And finally there must be particle to particle interaction. Since sound travels through a medium it causes the particles to move around and interact with one another.
Longitudinal waves are defined by the displacement of the medium traveling parallel to the propagation of the wave. A commonly used example is a slinky.
Pressure waves are closely related to longitudinal waves. Between each peak and valley in the wave there is compression and refractions happening. Compressions are areas of high pressure, where refractions are areas of low pressure. You can visually see this when looking at the image of the slinky. Where the coils are closer together the pressure is higher and when they're farther apart the pressure is lower. One way to quantity this idea is by the amount of pressure that varies relative to atmospheric pressure.