Short version: The bulk is encoded in the boundary.
Imagine a special circle. The border of this circle contains all the information of everything inside the circle, so the inside of the circle is a "holographic projection" of the information in the boundary.
In the same way that a holographic projection is physically two-dimensional, but contains enough data to appear three-dimensional from many different angles? (I'm guessing here, I don't really get holograms.)
A regular photograph captures the intensity pattern of light at a particular location at a particular time.
Holograms recreate the interference pattern of light in a volume of space. By interfering two coherent sources using a film that has the interference pattern captured, you recreate the interference pattern. Hence it exists in 3-D.
Imagine a special circle. The border of this circle contains all the information of everything inside the circle, so the inside of the circle is a "holographic projection" of the information in the boundary.