In ordinary light the vibrations are in all directions perpendicular to the path of motion of the light ray. In polarized light the vibrations can be in certain directions. It is actually the electric and magnetic fields that are waving, but these are difficult subjects also. At best we can give some simple indications of wave motion even though they don't apply so well to light and other electromagnetic radiation. It doesn't even require a medium.
Light can travel in a vacuum.
We can see the effects of the polarization of light by looking at polarized glasses. They have the greatest application of polarization. Place another polarized sheet on top of the first and rotate the top sheet until little or no light comes through from the projector onto the screen. Leave the polarized sheets in this configuration, because the polarizing angles are perpendicular to each other. Now place the plastic spoon between the two sheets and squeee the plastic fork in various places.