The low-level library Xlib is the client-side implementation of the X11 protocol. It communicates with an X server, but does not provide any function for implementing graphical control elements, such as e.g. buttons or menus. The Xt library provides support for creating and using graphical control elements, but does not provide any itself. Instead graphical control elements are implemented by other libraries using Xt, such as Xaw and Motif.
A programmer can for example use the Xt library to create and use a new graphical control element, e.g. a "two-side button". Since the graphical user interface of applications typically requires a number of graphical control elements, most are reluctant to write own ones, and instead rather use the ones provided by libraries such as Xaw and Motif.
Most modern toolkits such as FLTK, GTK+, and Qt do not use the Xt library, preferring to use Xlib or even XCB directly.