Defination of wave
A wave is a disturbance which propagates energy and momentum from one place to the other without the transport of matter.
One dimensional wave :
Energy is transferred in a single direction only.
Example : Wave propagating in a stretched string.
Two dimensional wave :
Energy is transferred in a plane in two mutually perpendicular directions.
Example : Wave propagating on the surface of water.
Three dimensional wave :
Energy in transferred in space in all direction.
Example : Light and sound waves propagating in space.