Transverse Wave
Definition
A wave where the medium vibrates side to side, perpendicular to the direction the wave travels — like a shaken jump rope.
Technical definition
A wave in which particle displacement is perpendicular to the direction of propagation, consisting of crests and troughs. Electromagnetic waves are transverse and need no medium at all.
Example
Flick one end of a rope up and down: the pulse travels horizontally down the rope while each bit of rope only moves vertically. Light from the Sun crosses 150 million km of empty space the same way — no medium required.
Transverse waves are not limited to ropes and water. Light is a transverse wave, which is why it can be polarized — and that polarization is impossible for longitudinal sound waves. The direction of vibration relative to travel is the whole distinction; the medium (or lack of one) is secondary.