GGI stands for General Graphics Interface, and it is a project that aims to develop a reliable, stable and fast graphics system that works on any platform.
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 
The GGI project provides various libraries. You don't need to use all of them, but the minimun are LibGGI and LibGII, upon which other packages depends.
The GGI site is http://www.ggi-project.org