waves

A wave is a disturbance that propagates (travels) through space and time, usually by transference of energy. A mechanical wave is a wave that propagates through a medium due to restoring forces produced upon its deformation. For example, sound waves propagate via air molecules slamming into their neighbors, which push their neighbors into their neighbors (and so on); when air molecules collide with their neighbors, they also bounce away from them (restoring force). This keeps the molecules from actually traveling with the wave.
Waves travel and transfer energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass transport. They consist instead of oscillations or vibrations around almost fixed locations. Imagine a cork on rippling water, it would bob up and down staying in about the same place while the wave itself moves outward. When we say that a wave carries energy but not mass, we are referring to the fact that even as a wave travels outward from the center (carrying energy of motion), the medium itself does not flow with it.
There are also waves capable of traveling through a vacuum, e.g. electromagnetic radiation (including visible light, ultraviolet radiation, infrared radiation, gamma rays, X-rays, and radio waves). They consist of period oscillations in electrical and magnetic properties that grow, reach a peak, and diminish to zero in a periodic fashion.