Depending on how the medium moves, waves are classified into three groups.

Transverse:
The medium moves perpendicular to the energy. This would be like a wave on a string where the energy is moving left to right, but the string itself moves up and down.

Longitudinal:
The medium moves parallel to the energy. Sound waves are longitudinal. As the energy moves left to right, the air molecules vibrate back and forth left and right. This makes high and low pressure areas instead of crests and troughs.

Surface:
This type of wave combines the properties of transverse and longitudinal. Picture a wave moving through the water. The wave moves the surface of the water up and down, but it also has a pressure change left to right.

Check out examples of the different types of waves at the following link:
Longitudinal and Transverse Wave Motion