Although it sounds like a strange form of martial arts, Script-Fu is in fact a scripting language that is part of the GIMP. With it, you can create scripts that automate a number of repetitive tasks to create desirable effects. When you created your logo, you might have noticed that a number of things were happening as it was being created. Try another logo and watch carefully what is happening. These steps are part of a Script-Fu script.
The GIMP comes with a number of Script-Fu scripts, and these are used for much more than just creating logos. Click Xtns on the GIMP toolbox, and scroll down to the Script-Fu menu. In addition to logos, you see options for creating buttons (for Web pages), custom brushes, patterns, and more. Play. Experiment. Don't be afraid.
Open an image. Then right-click on that image and scroll down to the Script-Fu part of the menu. Another menu drops down with selections such as Alchemy, Decore, Render, and so on. These are all pre-created effects that ordinarily require many repetitious steps. Script-Fu is very much like a command script, where one command follows another. In this case, the commands just happen to be graphical transformations.