A crest is the highest point on a wave, while a trough is the lowest point on a wave. In other words, a crest is a peak and a trough is a valley. These terms are often used to describe waves in the ocean, but they can also be used to describe other types of waves, such as sound waves or electromagnetic waves.
For example, when talking about ocean waves, the height of the wave from the surface of the water to the crest is called the wave's "amplitude," and the distance from one crest to the next is called the "wavelength." When the wave reaches its crest, it is moving up and has the most energy, while at the trough, the wave is moving down and has the least energy.
In other types of waves, such as sound waves or electromagnetic waves, the crest and trough represent the points where the wave has the highest and lowest amplitudes, respectively. For example, in a sound wave, the crest would represent the loudest point, while the trough would represent the quietest point.