The crest of a wave is the point of maximum positive displacement, or upward movement, away from equilibrium, or an undisturbed state. The opposite of "crest" is "trough," which is the point of the greatest negative, downward displacement.
Crests and troughs occur in transverse waves. A transverse wave is a wave where particles of the medium move in a direction perpendicular to the direction the energy is moving. There are three main components of a transverse wave: crest, trough and equilibrium. Amplitude of a wave is the distance the energy travels from equilibrium to crest/trough. Wavelength is the distance from one crest to the next.