The amplitude of a wave is important because it can tell you about the energy of the wave. The higher the amplitude, the more energy the wave has. For example, a wave with a high amplitude can cause more damage than a wave with a low amplitude.
The amplitude of a wave can also tell you about the medium through which the wave is traveling. For example, a wave with a high amplitude can travel through a dense medium more easily than a wave with a low amplitude.
Finally, the amplitude of a wave can also tell you about the source of the wave. For example, a wave with a high amplitude can be caused by a strong source, such as an explosion, while a wave with a low amplitude can be caused by a weak source, such as a gentle breeze.