GTK is an acronym for GIMP Tool Kit. It is a library of components for creating GUI applications written in C.
It is called the GIMP toolkit because it was originally written for developing the GNU Image Manipulation Program (GIMP), but GTK has now been used in a large number of software projects, including the GNU Network Object Model Environment (GNOME) project. GTK is built on top of GDK (the GIMP Drawing Kit), which provides an abstraction layer for the underlying windowing system functions. There is a third component called GLib, which provides the fundamental utilities used by GTK. These three libraries are synonymously referred to as GTK+.
Although GTK+ is written in C, there are GTK+ bindings for many other languages including C++, Guile, Perl, Python, TOM, Ada95, Objective C, Free Pascal, and Eiffel. GTK+ has also been ported to BeOS and Win32. These factors make GTK+ an excellent choice for a PHP extension that creates windowed applications.
Lastly, GTK+ is released under the GNU LGPL license, meaning that you can develop open software, free software, or even commercial non-free software using GTK+ without having to spend anything on licenses or royalties.