I don't know a whole lot about it, but GSI is "Generic System Image".
If a phone has proper "Treble" support and the bootloader is unlocked then it is theoretically possible to install a GSI image on it.
Treble is a design approach for Android that separates "Vendor implementation" from the "OS framework". The Vendor implementation being the kernel components and low-level hardware specific stuff.
This is primarily intended to be used by application developers who want to test out new OS interfaces without going out a buying a new phone or waiting for a updated Pixel to come or or something like that.
LineageOS and some other third party roms produce "Generic Images" that are intended to be used in this fashion.
Based on what I read it is very hit or miss in practice. Vendor specific hardware features might not work. So you might be without some bluetooth support or VoLTE support. This isn't really needed to test application OS features, so for people using GSI for development it doesn't really matter a whole lot.
This isn't really useful for projects like Graphene OS who want to be able to make kernel level changes and updates to their systems. You end up stuck with whatever the vendor provided and it isn't really a useful way to extend the usefulness of devices.
