A rack unit (abbreviated as U, less commonly seen as RU) is a unit of measurement applied to equipment racks and the servers, disk drives and other devices that they contain. One U is 1.75 inches (44.45mm); the standard rack, at 19 inches, is 42U.
Rack servers and other hardware designed to be rack-mounted are manufactured in multiples of 1.75 inches and specified in multiples of rack units, usually 1U, 2U, 3U or 4U. Racks are designed to hold equipment of those sizes. The holes in the mounting flanges of racks are arranged in groups of three, and that three-hole grouping is also called a rack unit.
Rack units for equipment is considered maximum dimensions. In practice, devices are often made slightly smaller than the specified U value to allow a little space. A device specified as 2U, for example, may in reality measure 3.44 inches in height, rather than the 3.5 inch multiple of 1.75.
See an introductory video on rack mounting equipment: