What is the gi.repository in python?

gi.repository is the Python module for PyGObject (which stands for Python GObject introspection) which holds Python bindings and support for the GTK+ 3 toolkit and for the GNOME apps.

See Projects/PyGObject on the GNOME Wiki.

It has nothing to do with GitHub.

It has nothing to do with github.

It is the Python API for GObject Introspection (gi). The repository portion is related to the repository of bindings available via GObject Introspection (girepository).

Importing bindings via this method is what replaces the old straight Python bindings for gobject, glib, gtk and similar libraries.