transverse wave
Flick the end of a long rope up and down and a hump races along the rope toward the far end, yet the rope itself never moves toward that end, each bit just goes up and down. A transverse wave is one where the wiggling is sideways to the direction the wave travels. The question it answers is: which way do the particles move compared with the direction the wave is going?
In a transverse wave the particle displacement is perpendicular (at right angles) to the direction the wave travels. Picture crests (the high points) and troughs (the low points) moving along, while each piece of the medium moves across the line of travel, up and down or side to side, as the crest pattern advances. Because the motion has a definite sideways direction, transverse waves can be polarized, meaning restricted to a single plane of vibration. Waves on a string, ripples on water (roughly), and light are all transverse.
An honest caveat: a transverse mechanical wave needs a medium that resists shearing (bending sideways), which is why such waves travel through solids and along surfaces but not through the bulk of a gas or liquid. That is exactly why sound in air is not transverse. Light is transverse yet carries no medium at all, what oscillates crosswise there are the electric and magnetic fields.
Shake a stretched slinky or rope from side to side. The wave races along its length while each coil only swings across the line of travel, sideways motion, forward travel.
In a transverse wave, particles move at right angles to the wave's travel.
Only transverse waves can be polarized. Sound in air cannot, because it is longitudinal, not transverse.