A 19-inch rack is a standarized system for mounting various electronics in a "stack". A rack is any long plate with holes drilled in it (cf. rack and pinion steering), and in this case the rack-mount consists of four standardized racks mounted in two sets 19 inches apart, one set for the front and rear of a large box-shaped enclosure.
Equipment can be mounted directly to the rack by screwing into the holes. It is also common to mount a set of rollers on the rack, and then have the equipment simply slide in and out on the rollers for easy access. In this case the equipment still uses large thumbscrews in the front to keep it from sliding out.
Equipment designed to be placed in a rack are typically referred to as rack mount or a rack mounted system. The vertical depth of 19-inch rack equipment is usually a multiple of a standard unit of height called the 'U', meaning Unit, whose dimensions were originally developed for a horizontal rack mounting system known as Eurocard. A 1 U is 1.75 inches (44.45 mm).
This standard rack arrangement is widely used throughout the telecommunication, computing, audio and video industries, as well as others.