Holographic principle states that information encodes reality into matter/energy and gravity. Basically gravity, matter and energy are sideffects of information. They are its projections.
How does this relate to hologram? Well dots that might appear like two separated dots on the 3D model, could be encoded on the 2D surface as very close. What this explains is "spooky action at a distance". We perceive two entangled electrons as being far away on a reality hologram, when in reality they are close on the fundamental 2D picture of the world.
Summary: What we perceive and measure as reality is not what reality fundamentally is.
NOTE: This is extremely layman termish and don't be too surprised if it's wrong. I last read UiaN years ago. There are also some other interesting properties, like that the any part of hologram contains whole picture of hologram but of lousier quality, etc.
2) I think Universe in a Nutshell covers most of this theory pretty well.