Waves are vibrations that transfer energy from place to place without matter - solid, liquid or gas - being transferred.
In transverse waves, the oscillations (vibrations) are at right angles to the direction of travel and energy transfer. Water waves are transverse waves.
A mexican wave is generally seen among football spectators where The wave moves around the stadium, while each spectator stays in their seat - only moving up, and then down, when it is their turn.
Mexican wave can be regarded as an example of transverse wave