Amp rack is short for amplifier

Amplifier

Generally, an amplifier or simply amp, is a device for increasing the power of a signal.In popular use, the term usually describes an electronic amplifier, in which the input "signal" is usually a voltage or a current. In audio applications, amplifiers drive the loudspeakers used in PA systems to...

 rack and is a term used mostly in reference to professional audio

Professional audio

Professional audio, also 'pro audio', refers to both an activity and a type of audio equipment. Typically it encompasses the production or reproduction of sound for an audience, by individuals who do such work as an occupation like live event support, using sound reinforcement systems designed for...

 applications to describe any furniture, fixture, or case where amplifiers are mounted by their faceplates or in slot grooves, mostly synonymous with rack mount.

Examples include use in recording studios, mobile DJ setups, or live stage events. Each of these instances could require more power or more output channels than a single amp could provide, but necessitate portability of all amps at once.

The term is also sometimes used to describe the mounting fixture of an amp or amps used in car audio

Car audio

Car audio/video , auto radio, mobile audio, 12-volt and other terms are used to describe the sound or video system fitted in an automobile. While 12-volt audio and video systems are also used, marketed, or manufactured for marine, aviation, and buses, this article focuses on cars as the most common...

 applications, though usually not the 19" rack mount variety.