A wave is an oscillation that transfers energy. It may or may not move through a medium such as air or water. Certain types of waves, referred to as mechanical waves can only propagate in a medium. Electromagnetic waves may propagate through anything, including a vacuum like space.
A mechanical wave such as sound (also a type of longitudinal wave) or a wave associated with a body of water (a type of surface wave) are those that require a medium (matter) to propagate. The energy that is propagated by the wave moves in the same direction as the wave. Mechanical waves need an initial input of energy.
Reflection is one of several different types of interactions that can occur when a wave encounters a boundary. When a wave is reflected off a boundary surface, its angle of the reflected waves is equal to the angle of the incident wave, both with respect to the normal.