Sound Waves are Longitudinal Waves
Take a slinky. Mark a dot on it. Fix one end to a wall. Hold the other end. Give it a sharp push towards the wall. You will notice the dot move back and forth, parallel to the direction of propagation of the disturbance. There are regions where the coils of the slinky are pressed close to one another (compressions) followed by regions where the coils are further apart (rarefactions). This is how a sound wave also travels.
The particles of the medium just oscillate about their mean position. Hence sound waves are longitudinal in nature.
Another type of wave is called transverse wave. Light rays, electromagnetic waves are all transverse in nature. In this type of wave, the particles of the medium move about their mean position, in a direction perpendicular to the direction of propagation of the wave.
Both longitudinal and transverse waves are mechanical waves.