The trough is the lowest point of a wave. A wave is a type of disturbance that transmits energy through a medium from one specific position to another. A transverse wave is the type of wave where there are these high and low points.
A transverse wave is one in which the medium's vibrating element moves at right angles to the direction of its propagation. The medium can be water or a rope. Along with troughs, transverse waves have high points called crests. Some other characteristics of transverse waves are their amplitudes, frequencies and wavelengths.
A wave's amplitude is measured from the top of the crest to the rest position of the medium. The amplitude gives the maximum displacement. The frequency is how many waves move through a given point within a certain interval of time. The wavelength is the distance between either two adjacent troughs or two crests.