If medium particles oscillate up and down about their rest positions in a direction perpendicular to the direction of propagation of the wave, then the wave is called transverse wave. For example, light is a transverse wave.
BUT IN THE CASE OF LIGHT, THERE ARE NO MEDIUM PARTICLES THAT VIBRATE. SO, HOW CAN IT BE CALLED A TRANSVERSE WAVE ?
Electromagnetic waves are type of transverse wave which does not require any material medium for there propagation.
In this electric field vector and magnetic field vector both oscillates in a direction perpendicular to the propagation of the wave. That's way electromagnetic wave is transverse in nature.