Laser light is much purer than the ordinary light in a torch beam. In a torch beam, all the light waves are random and jumbled up. Light in a torch beam runs along any oldhow, like schoolchildren racing down a corridor when the bell goes for home time. But in a laser, the light waves are coherent : they all travel precisely in step, like soldiers marching on parade.
When a las...er beam is split up to make a hologram, the light waves in the two parts of the beam are travelling in identical ways. When they recombine in the photographic plate, the object beam has travelled via a slightly different path and its light rays have been disturbed by reflecting off the outer surface of the object. Since the beams were originally joined together and perfectly in step, recombining the beams shows how the light rays in the object beam have been changed compared to the reference beam. In other words, by joining the two beams back together and comparing them, you can see how the object changes light rays falling onto it—and that's simply another way of saying "what the object looks like." This information is burned permanently into the photographic plate by the laser beams. So a hologram is effectively a permanent record of what something looks like seen from any angle.
Now this is the clever part. Every point in a hologram catches light waves that travel from every point in the object. That means wherever you look at a hologram you see exactly how light would have arrived at that point if you'd been looking at the real object. So, as you move your head around, the holographic image appears to change just as the image of a real object changes. And that's why holograms appear to be three-dimensional. Also, and this is really neat, if you break a hologram into tiny pieces, all the pieces still contain enough information to recreate the complete hologram: smash a glass hologram of a cupinto bits and you can still see the entire cupin any of the bits!