A wave is a transmission of a disturbance from one point to another. It involves movement of energy from the source to another.
Waves may be classified as mechanical waves or electromagnetic waves depending on whether they require material medium for transmission.
Electromagnetic waves are those waves that do not necessarily require a material medium for transmission, that is they can be transmitted even in a vacuum. Such waves include, x-rays, radiowaves, microwaves, etc.
Mechanical waves on the other hand require a material medium for transmission. Such waves include sound waves.