This page was written right after this wiki was introced, more to play around and get this thing started than because I have so much to say about GiGi. More knowledgable people please add to this.
The GiGi development library (sometimes called GG) is used by FreeOrion to handle most of the basic UI and graphics things (windows, fonts, input, images, and such). It uses (at least in this project) SDL internally for platform-dependant things, and OpenGL for graphics.
Sourceforge page: http://sourceforge.net/projects/gigi