We observe in nature that when we have an elastic medium, a disturbance originating at one point can be propagated to another point in the medium. This mechanism for transfer of energy or momentum is called wave.
For example, the water surface (of a pond, let’s say) is kind of like an elastic sheet. A disturbance caused by a falling rain drop will be propagated outward. The energy of the fallen rain drop is carried outward along water surface by a circular wave. You must realize that the water does not travel with the wave. In fact, every drop of water in the wave merely oscillates about its own equilibrium position. Water merely serves as the medium in which a wave can propagate energy along.
Similarly, if you hold one end of a rope and swing your hand up and down continuously, you can send a wave traveling down the rope. Again, notice that each section of the rope merely oscillates about its own equilibrium position. As always, the particles in the wave medium do not travel with the wave, only the energy is passed along.
Now, if your hand’s up and down motion is simple harmonic, the wave generated will be sinusoidal in shape.
The H2 syllabus is mainly concerned with sinusoidal waves. The cute thing about sinusoidal waves is that every point on a sinusoidal wave is itself a sinusoidal oscillation, i.e. simple harmonic motion. The frequency f of the wave is simply the frequency of the SHM. The wavelength λ of the wave is simply the distance occupied by one complete sinusoidal cycle of the wave.