The image of waves is helpful in understanding the happenings we observe while we meditate.
Everything that comes to be passes away. In terms of consciousness or the mind, this is easily observable. Sensations, thoughts, images and emotions appear and disappear. This ceaseless change is a fundamental truth in Buddhism. Without training, we tend to see whatever happens as being more or less continuous. We may realize that our sensations, thoughts, imagery and emotions come and go, but we think that they last for a noticeable period of time, perhaps a second, minute, hour, day or even several days. I am angry, and I have been angry for days. I am happy, and I think that my happiness has been with me for some time. But in Buddhist psychological theory, all these things occur in moments of extremely brief duration, on the order of nanoseconds. Furthermore, there can be only one happening in consciousness at any given time. So if we think that any of these happenings occur over an extended period of time, we are mistaken. A happening comes to be and quickly passes away to be replaced by another happening, which may be so similar to the previous happenings that we do not realize that it is a discrete happening.
The image of a wave is useful because it captures the rising and falling of these discrete happenings. Waves have properties of amplitude (how big they are) and frequency (how fast they occur). There are big slow waves, small slow waves, big fast waves, small fast waves and everything in between.
We can think of the discrete happenings that occur while we meditate in terms of these waves. We have to be very alert to see the rising of the wave and to observe the passing away. If we push away the happenings as they appear, we do not see them pass away on their own. The time frame is crucial. In the beginning of practice, a thought or emotion may seem to be present for several seconds or minutes. Perhaps they linger. We could push them away, but that would be a form of avoidance or suppression. We should let them go as they fade away. This makes letting go so much easier.
In terms of waves, these happenings are very small in amplitude and very fast in their frequency. But the untrained mind tends to experience them as big and rather slow waves depending on how strongly experienced they are and how long they seem to hang around. The trained mind with wisdom would experience them more as they are, as discrete and momentary (although it may be nearly impossible to experience them at the speed in which they actually occur).
As you meditate, see if this idea of waves is helpful. You can practice with your breath or abdominal movement or with any of the happenings that arise and pass away. You will find that noting is a way of catching the wave, and, as you note, you should see the wave fading away, in which case you can return to focusing on the breath or abdominal movement or you can catch the next happening wave.