1- Waves can be viewed as a disturbance in the medium around an equilibrium state, which is generally at rest. The energy of this disturbance is what causes the wave motion. A pool of water is at equilibrium when there are no waves, but as soon as a stone is thrown in it, the equilibrium of the particles is disturbed and the wave motion begins.

2- The disturbance of the wave travels, or propogates, with a definite speed, called the wave speed (v).

3-Waves transport energy, but not matter. The medium itself doesn't travel; the individual particles undergo back-and-forth or up-and-down motion around the equilibrium position.

in reference to:

"The disturbance of the wave travels, or propogates, with a definite speed, called the wave speed (v). Waves transport energy, but not matter. The medium itself doesn't travel; the individual particles undergo back-and-forth or up-and-down motion around the equilibrium position."
- Mathematical Properties of Waves (view on Google Sidewiki)