GGI stands for "General Graphics Interface", and it is a project that aims to develop a reliable, stable and fast graphics system that works everywhere. We want to allow any program using GGI to run on any platform requiring at most a recompile.
It all started out with some people being annoyed by the fact that graphics in Linux means either X or svgalib, and if you use both at the same time, you can easily crash the graphics card and make the system unusable. Nowadays, GGI development also involves a portable userspace library, 3D graphics, and anything else that is fun to hack :-)
For a more detailed explanation, please visit the Documentation pages.