GTK - Wikipedia

Actually I don't know what is meant by Gtk in the cannot open display warning.

    (hull:2647): Gtk-WARNING **: cannot open display:

So I wikied as cut and pasted below.

GTK+ (GIMP Toolkit) is a cross-platform widget toolkit for creating graphical user interfaces. It is licensed under the terms of the GNU LGPL, allowing both free and proprietary software to use it. It is one of the most popular toolkits for the X Window System, along with Qt.[1]

The name GTK+ originates from GTK; the plus was added to distinguish an enhanced version.[2] It was originally created for the GNU Image Manipulation Program (GIMP), a free software raster graphics editor, in 1997 by Spencer Kimball and Peter Mattis, members of eXperimental Computing Facility (XCF) at the University of California, Berkeley. It is now maintained by members of the GNOME Foundation.

Design

GTK+ is an object-oriented widget toolkit written in the C programming language; it uses the GLib object system for the object orientation. On the X11 display server, GTK+ uses Xlib to draw widgets. Using Xlib provides flexibility and allows GTK+ to be used on platforms where the X Window System is unavailable. While GTK+ is primarily targeted at the X Window System, it works on other platforms, including Microsoft Windows (interfaced with the Windows API), and Mac OS X (interfaced with Quartz). HTML5 and Wayland backends are in development.

GTK+ can be configured to change the look of the widgets drawn; this is done using different display engines. Several display engines exist which try to emulate the look of the native widgets on the platform in use.

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Desktop Environments that use GTK+

GNOME is based on GTK+, meaning that programs native to GNOME use GTK+

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LXDE (Lightweight X11 Desktop Environment) is based on GTK+


Applications

Some notable applications that use GTK+ as a widget toolkit include:

Chromium – Linux version of the web browser developed in large part by Google

Firefox – Linux version of the web browser developed by Mozilla

Midori – Minimalistic web browser utilizing GTKWebKit as rendering engine and GTK+ as widget toolkit

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I also don't know exactly what is a widget.  The wiki says the following.

Software widget, a generic type of software application comprising portable code intended for one or more different software platforms

Widget toolkit, a software library containing a collection of GUI widgets that collaborate when used in the construction of applications

Web widget, an applet intended to be used within web pages

GUI widget, in computer programming, a reusable element of a graphical user interface

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