Interference is the where the apparent brightness of light changes depending on the light having the same or different phases. If the phases of two beams of light match, their intensities add up and they appear brighter; this is called constructive interference. When the two beams are out of phase, they produce a lower intensity when joined and this is known as destructive interference.
Schematic of constructive and destructive interference
Laser Interferometry and White Light Interferometry are two examples of techniques using this phenomenon. In both cases, the phase of light is used to generate bright and dark spots. As coherent light propagates down the optical path, the phase oscillates. The phase oscillation allows for changes in distance to be measured.
By splitting the same light into two different paths with a beam splitter, you can then recombine the light to determine how far one path is compared to the other. Light that has traveled the exact same distance will be bright, while light that has traveled a slightly different length will be darker.
Schematic for interferometry
This is generally used to create a pattern of bright and dark areas in an image that can then be used to create a three dimensional reconstruction of the surface. It can also be used as a point scanning technique where the highest brightness is maintained and the surface is scanned in X, Y and Z. The movements of the stage or optics are monitored in order to recreate the surface.