The way a transverse wave works is that the oscillations of the wave is perpendicular to the direction of the actual wave itself. Consider the example of a drum, where hitting the top of the drum creates ripples to expand from the center of the collision but these ripples move up and down instead of in the same direction. For light, the displacement of particles is perpendicular to the direction of propagation. The oscillations are the electric and magnetic fields, which point at right angles to the light rays from the initial location.