It's GSettings, which is where GTK+ apps usually store their settings. You'll find a lot if you google that name, but here's GNOME's page about it.
It's often compared with the Windows registry, but to me it's much more like MacOS's
defaults system which it inherited from NeXTSTEP.
It's actually a couple layers. The backend that is essentially always used is
dconf (hence the graphical dconf Editor), and Gsettings is a layer above it that is what you usually want to use. If I understand correctly, GSettings required schema, basically a description of what options there are and what values they can take, while dconf is the raw store. So with GSettings you can make an option and define what the possible values are, like Brisk Menu's search field being at the top or bottom. GSettings only lets pick top, bottom or auto. If you edit the value directly with dconf, you could set it to blue or 1.875 which would make no sense to the app.