A wave is a disturbance that transfers energy and momentum from one point to another in a medium.
For example, the wave of the ocean moves in medium water and we can see the movement of the wave crest from one side to the other side in a given time period.
When a wave travels in a medium, the particles vibrate about their mean position transferring energy to the neighbouring particle without leaving their original place.
Some of the waves do not require a medium for their propagation. These waves are called non-mechanical waves. e.g. electromagnetic waves.
Waves can be classified:
Transverse wave: in this, the particles of the medium vibrate in a direction perpendicular to the direction of propagation of the wave.
Longitudinal wave: in this, the particles vibrate in the same direction as the propagation of a wave.