In the Personal Quarters, two terminals are available:
The Quarter Upgrades, and the Income Generators.

The Personal Quarter also features some purely cosmetic interior like a bed, a little kitchen section, a workbench with tools and various weapons on it, as well as a corner with couches and a table with a dancing Robot hologram on it which players can interact with. The Quarter Upgrades Terminal is positioned on a table on the left side of the wall after the workbench. The Income Generator Terminal is positioned on the right side of the wall before the little couch section.

The TV in the couch area features trailers of the original Cycle game.
Looking out of the window, one can see that the quarters are above the Leafman's Bar, roughly 7 stories up.

(source: thecyclefrontier.wiki)

This value describes the overall level of the Personal Quarters. In order to upgrade this, players need to research upgrades in the trees first.

Every 23 hours, a Supply Crate with a random collection of Weapons, Gear and Consumables can be claimed. The available items depend on the Level of your crate, which can be increased with Quarter Upgrades. The 23h timer to the next one starts at the moment the Crate is claimed.

This upgrade shorten all Personal Quarters Upgrade Times by a percentage. Each upgrade makes this timer shorter.

Special dedication to the official wiki that i shamefully copypasted with help from Greenshot, Paint, and Gimp.

Luck be with you, prospectors !