At the heart of a digital light processing projector is a digital micromirror device. Its surface contains a dense array of tiny mirrors, each able to tilt to steer incoming light toward or away from the projection lens.
A mirror for each picture element
A controller switches mirrors rapidly. The share of time a mirror directs light toward the lens controls the brightness of the corresponding picture element. Color can be supplied by timed red, green and blue illumination or by separate optical paths, depending on the design. The viewer sees the combined image rather than the individual mirror movements.
From switching to color
The chip reflects and modulates light; it is not a light source by itself. Lamp, LED or laser illumination, optics and screen conditions all affect final brightness and color. A DLP system is therefore an example of micro-scale mechanics used to control light at human scale.
Related: how a laser produces a narrow coherent beam.