As I read it, the book doesn't say the Universe IS a hologram, merely that it is LIKE a hologram in a number of ways. The properties which govern the behavior of matter vary depending on the scale at which you make an observation. For example, you can calculate the motion of a planet or comet using Newtonian physics. However, if you attempt to observe something such as an electron or photon, Newtonian physics breaks down utterly. Sometimes, particles such as these actually combine with other particles to become something different altogether, a type of behavior not possible with a planet.
Saying that the Univese is LIKE a hologram is a way of saying that there is more to the Universe than that which meets our senses. Our eyes see visible light within a certain range of wavelengths, usually between 4000 and 7000 nanometers. Objects which emit or reflect light outside this range are entirely invisible to us, yet they exist nonetheless. Many other beings on this planet see considerably further into the infra-red range, or into the ultra-violet range, than we are capable of. What would the night sky look like to, say, a bee, with its extended ultraviolet vision?
There used to be an expression, saying that "(This or that) has nothing to do with the price of tea in London", implying that one thing had nothing to do with another thing. However, as more information becomes available, it does seem apparant that all things are connected in an interdependent web of existence. On the scale of the very tiny, experiments shooting individual photons of light through slots in metal indicate that somehow, photons can 'detect' what another photon is doing, even at a distance. This implies that they are connected in some way that we don't fully understand? On the scale of the very large, the mere presence or absence of a massive body at the right location in space can visibly affect the motion even of stars. This was one of the ways that planets were first detected around some of our neighboring stars. As planets orbited those stars, their own gravity would induce a 'wobble' in the star around which they moved, demonstrating their existence even though they could not be seen in the glare of the star itself. Objects such as black holes are invisible under visible light, however they can be 'seen' by their strong gravitational disturbance on other bodies. 'Dark Matter' is also invisible, yet its mass can be detected, and its presence has profound significance on whether or not the Universe will continue to expand forever, or eventually collapse back into a singularity.
The influence of small actions on the large scheme of things was beautifully illustrated in a famous short story by Ray Bradbury titled 'A Sound Of Thunder', in which the death of a single butterfly has dramatic consequences which reach over many millions of years. The basic idea of this story is the foundation for the current movie 'The Butterfly Effect'.