In the animation that precedes this one we imagined sending a wave train down a rope. That animation showed only one tiny section of the rope. Here, in this animation, imagine the several yellow boxes to each be a tiny section along the length of the rope.
You should be able to visualize the wave shape moving from the left to the right. However, be sure to realize that all of the yellow boxes, that is, all the small sections of the rope, are moving up and down.
Each small section of rope moves up and down with vertical simple harmonic motion. Each vertical simple harmonic motion is slightly shifted from its neighbors. The combined vertical simple harmonic motion of each small section generates the horizontal wave motion.
The wave moves from the left to the right horizontally. However, the medium moves up and down.
This is the central concept to the definition of a transverse wave.
A transverse wave is a wave with the motion of the medium being perpendicular to the motion of the wave. More carefully, we would say that the direction of the velocity of the medium is perpendicular to the direction of the velocity of the wave.
Often, when everyone in the conversation understands the details, we simply say that a transverse wave is a wave with the disturbance perpendicular to the propagation.