Diffraction gratings work because light behaves like a wave. If two peaks line up, the light is amplified, and if a peak and a valley line up, the light is cancelled. Where the light is in this peak/valley cycle is called the light's phase. If we can control the phase of the light, we can control where the peaks and valleys line up, and use this to steer the light to produce 3D images.

 

There are many different types of holograms which control the phase of light in different ways. You can control it by making some of the light reflect off a surface slightly before or after the rest of the light using a bumpy shiny surface, you can use a bumpy clear surface to cause some of the light to be slowed down for longer than the surrounding light, advancing its phase more, or you can use a speckley surface where some of the light is opaque and the rest is clear to just get rid of the light where it has the wrong phase. Visible light has a wavelength of only a few hundred nanometers, so these bumps are usually too small to see without an electron microscope.