Think of a rope:
* Transverse wave: If you shake the rope up and down, the waves travel horizontally along the rope, but the rope itself moves vertically (perpendicular to the wave direction).
* Longitudinal wave: If you shake the rope back and forth, the waves travel horizontally along the rope, and the rope itself also moves horizontally (parallel to the wave direction).
So, in a transverse wave, the particles of the medium oscillate perpendicularly to the direction of wave propagation.