Does anyone here know more details?
Gallium is an interface for doing 3D stuff. It's very generalized and describes a very general, shaderful, batched renderer. "Shaderful" means that the renderer has shaders instead of old-school fixed-function TCL and pixel combiners; "batched" means that the renderer prefers to operate on pre-cooked buffers full of data rather than vertex-at-a-time data.
Gallium matters because it is a much more direct and low-level interface for describing hardware which enables hardware-specific optimizations to be decoupled from API-level logic. We have implemented GL, D3D (not open-source!), VG, X11 (EXA, Xv, XvMC, VDPAU), etc. on top of Gallium, without having to write entirely new backends each time. It makes it easier to write drivers. Gallium's actual interface is also less verbose than user-level APIs, which means the actual drivers are smaller by anywhere from 30-50% LOCs.