The disturbance is perpendicular to the direction of the wave motion (propagation direction).
Best visualized on a rope whose one end you start agitating. This gives rise to waves running (propagating) forward, away from that end. While that is happening, if you look at the individual points on the rope you will see that they are not moving in the forward direction but rather they oscillate up and down (disturbances). The up-down direction is perpendicular to the direction of the forward wave propagation.
