Transverse waves can oscillate in any plane. Polarisation is the process by which the oscillations are made to occur in one plane only.
This is done by passing the waves through a 'grid' so that only the waves that can fit through the slits can continue through:
This idea is used in Polaroid glasses to reduce the amount of light able to reach the eye. Polarisation also has to be taken into account when transmitting and receiving waves. An aerial has to be aligned to the plane of the polarised waves for it to receive the maximum signal.
You should be able to describe experimental demonstrations with both light and microwaves.
Polarisation can also be achieved by creating waves in one plane (for example, a laser).
Longitudinal waves cannot be polarised.