The light-sensitive emulsion used to create holograms makes a record of the interference between the light waves in the reference and object beams. When two wave peaks meet, they amplify each other. This is constructive interference. When a peak meets a trough, they cancel one another out. This is destructive interference. You can think of the peak of a wave as a positive number and the trough as a negative number. At every point at which the two beams intersect, these two numbers add up, either flattening or amplifying that portion of the wave.
This a lot like what happens when you transmit information using radio waves. In amplitude modulation (AM) radio transmissions, you combine a sine wave with a wave of varying amplitudes. In frequency modulation (FM) radio transmissions, you combine a sine wave with a wave of varying frequencies. Either way, the sine wave is the carrier wave that is overlaid with a second wave that carries the information.
In a hologram, the two intersecting light wave fronts form a pattern of hyperboloids -- three-dimensional shapes that look like hyperbolas rotated around one or more focal points. You can read more about hyperboloidal shapes at Wolfram MathWorld.
The holographic plate, resting where the two wave fronts collide, captures a cross-section, or a thin slice, of these three-dimensional shapes. If this sounds confusing, just imagine looking through the side of a clear aquarium full of water. If you drop two stones into the water at opposite ends of the aquarium, waves will spread toward the center in concentric rings. When the waves collide, they will constructively and destructively interfere with each other. If you took a picture of this aquarium and covered up all but a thin slice in the middle, what you'd see is a cross-section of the interference between two sets of waves in one specific location.
The light that reaches the holographic emulsion is just like the waves in the aquarium. It has peaks and troughs, and some of the waves are taller while others are shorter. The silver halide in the emulsion responds to these light waves just like it responds to light waves in an ordinary photograph. When you develop the emulsion, parts of the emulsion that receive more intense light get darker, while those that receive less intense light stay a little lighter. These darker and lighter areas become the interference fringes.
In the next section we'll look at the emulsion bleaching process.