Motif is a GUI toolkit for X. It dates back to the 1980s, and is one of the components of the Common Desktop Environment.
Motif was commonly used by GUI developers in the early days of GUI interfaces. With the advent of GTK and Qt, Motif has fallen out of common use.
Motif is also not open source software, although a version exists that allows free use of Motif in developing software for open source environments, and an open source clone Lesstif licensed under the LGPL is available.