Transverse wave motion is the beautiful rippling effect that occurs when a moving wave causes oscillations that travel perpendicular to the direction of energy transferred. (For example, via Wikipedia: "If a transverse wave is moving in the positive x-direction, its oscillations are in up and down directions that lie in the y–z plane.")
See it demonstrated in slo-mo in the video below:
Anybody can create a transverse wave quite easily—all you need to do is solidly anchor one end of a string, and while holding it semi-taut, create waves by moving the free end in an up-and-down motion.
To illustrate and emphasize the theory in a larger, hands-on scale, the National STEM Centre and the Institute of Physics have produced the below video, in which Alom Shaha explains how to make your own wave machine using tape, wooden skewers and jelly candy. Download project notes here.