Usually when we think of waves, we think of transverse waves. These are waves where points move up and down perpendicular to the motion of the wave. Examples include water waves, whipping a rope, or even doing the "wave" in a crowd. You can think of these as "two dimensional" waves.
Longitudinal waves are waves where points move left or right, parallel to the motion of the wave. In other words, there is compression and expansion of the medium. Examples include sound waves, or pulses in a slinky.
