GUI stands for Graphical User Interface. A GUI is a fundamental component of many (but not all) modern computer applications and systems. It is largely what it sounds like, a graphical (with textual components) front-end for a human user to interact with a piece of software. All Creatures games have a GUI, without one it is not really possible to play the game at all. The type of GUI varies according to the engine being used.
Regarding the original engine used by C1 and C2, these games ran in windowed mode and functioned much like a typical piece of Windows (or Mac OS) software at the time (think for example office software) - containing menus, dialog boxes and the like. From these a user could select their norn, open and close applets, scroll around the world, perform standard application functions like opening and closing the game, and so on...
In the newer engine used by C3, DS, and CV, the game by default ran in full screen mode or could instead be run windowed as a simple box on the desktop. It did not contain any Windows-style menus, instead all functions were coded via CAOS and appeared as part of the world, often with no clear distinction between a GUI element and a piece of complex machinery in the world. Examples of this type of GUI element include the heads up display and volume controls. As such, there were no applets, instead there would be sets of machinery e.g. the medibay standing in for the science and health kits, or muco/egg layer instead of the hatchery. CV had a similar system, modified for its younger target audience. In these games, even the world launchers were coded via CAOS and essentially ran as separate "worlds" of their own prior to loading the selected full world. External third party "applets" could be run outside the game with a more conventional (to the earlier games) type of GUI.
Even the hand or pointer, avatar of the player, can be considered a GUI element. (Technically, it could be argued that any interactive, visual element present in the game is part of a GUI, but that is not what is meant here...)