The best way to discover GeeXLab (as well as GLSL Hacker) is to study the code samples. Source codes are provided and they are ready-to-use: just drag and drop the XML file in GeeXLab (drag'n'drop on Windows and macOS only). You can download them from this page: Code Sample Pack.
The XML Host-API is the set of xml nodes that allows to describe a 3D scene.
The Scripting Host-API is the set of modules and functions that allows Lua and Python scripts to interact with GeeXLab engine.