Suppose that same slinky is now stretched out horizontally and a pulse is introduced by vibrating the first coil up and down.
A pulse of energy will be carried through the slinky from left to right and the coils will move up and down.
The displacement pattern moves the particles of the medium perpendicular to the direction of the pulse.
Waves traveling through a solid medium can be either transverse waves or longitudinal.
Waves traveling through fluid or gas (air) are always longitudinal.
Transverse waves require a rigid medium to transfer their energy.