If you throw a pebble into a pond, ripples spread out from where it went in. These ripples are waves travelling through the water. The waves move with a transverse motion. The undulations (up and down movement) are at 90° to the direction of travel.
For example, if you stand still in the sea, the water rises and falls as the waves move past you.
The slideshow shows how you can model transverse waves using a rope: