The highest part of the wave is called the crest. The lowest part is called the trough. The wave height is the overall vertical change in height between the crest and the trough and distance between two successive crests (or troughs) is the length of the wave or wavelength.
While one normally associates an up and down motion with the passage of each wave. Actually, a circular motion occurs. It is this orbital motion of the water (or objects on the surface of the water) that causes an object to bob up and down, forward and backward as waves pass under it.
But even this motion is not exactly circular but is trochoidal (line form traced by a point on a rolling wheel). While the motion in a wave over deep water move is an almost closed circular path there is a tiny forward motion with the passage of each wave, particularly in large waves.
Also, the motion changes as the depth increases. The trochoidal flattenes with increaseing depth as well as a decrease in the total motion. This flattening of motion/decreasing size continues with increaseing depth until all that remains is a small back and forth movement and even that will cease to be noticed.