Here's a way to visualize it:
* Imagine a rope tied to a wall.
* If you shake the rope up and down, you create a wave that travels along the rope.
* The wave travels horizontally (parallel to the rope), but the rope itself moves vertically (perpendicular to the direction of the wave).
This is the key characteristic of a transverse wave – the disturbance (the vibration) is at a right angle to the direction the wave travels.