The microscopic interference fringes on a hologram don't mean much to the human eye. In fact, since the overlapping fringes are both dark and microscopic, all you're likely to see if you look at the developed film of a transmission hologram is a dark square. But that changes when monochrome light passes through it. Suddenly, you see a 3-D image in the same spot where the object was when the hologram was made.
A lot of events take place at the same time to allow this to happen. First, the light passes through a diverging lens, which causes monochromatic light -- or light that consists of one wavelength color -- to hit every part of the hologram simultaneously. Since the hologram is transparent, it transmits a lot of this light, which passes through unchanged.
Regardless of whether they are dark or clear, the interference fringes reflect some of the light. This is where things get interesting. Each interference fringe is like a curved, microscopic mirror. Light that hits it follows the law of reflection, just like it did when it bounced off the object to create the hologram in the first place. Its angle of incidence equals its angle of reflection, and the light begins to travel in lots of different directions.
But that's only part of the process. When light passes around an obstacle or through a slit, it undergoes diffraction, or spreads out. The more a beam of light spreads out from its original path, the dimmer it becomes along the edges. You can see what this looks like using an aquarium with a slotted panel placed across its width. If you drop a pebble into one end of the aquarium, waves will spread toward the panel in concentric rings. Only a little piece of each ring will make it through each gap in the panel. Each of those little pieces will go on spreading on the other side.
This process is a direct result of the light traveling as a wave -- when a wave moves past an obstacle or through a slit, its wave front expands on the other side. There are so many slits among the interference fringes of a hologram that it acts like a diffraction grating, causing lots of intersecting wave fronts to appear in a very small space.