The specified dimensions are width (48.26 cm = 19 inch) and height (multiple of 4.445 cm). Because the width is 19 inch, the rack that meets this requirement is sometimes called "19 inch rack". The basic unit of thickness is 4.445cm. 1u is 4.445cm, 2u is 8.89cm, which is twice as much as 1u (and so on).
U is not a patent of the server, it was originally a rack structure for communication exchange, referring to the rack of the server. At present, it is used as an unofficial standard in frame structure, including the specified screw size, hole spacing, track marking and so on.