Well, it's aquaponics, so the green tray is actually a lava rock or hollow clay bead garden - it acts as the aquarium's filter. The media are colonized by nitrifying bacteria from the air, which turn the ammonia the fish produce into nitrates that can feed plants (which you also seed in the lava rock). That way the water is cleaned as it flows through the system, and you can grow a whole host of plants in the green tray. The water's pouring into the surface of the fishtank part is enough to oxygenate it. The reason it has a siphon that periodically fills and drains it is that most plants will rot if their roots are continuously embedded in water.
The VERY top tray is for a big lamp to provide artificial sunlight to the plants, because my apartment gets terrible light, particularly in the winter!
It was a term -fully it was hydrostatic pressure- that I saw when I read about the Pythagorean cup. Of which, the same design/principle is at play here when the water flows back into the main tank. It's fascinating how it works. (No, I am not smart, I have not the motivation to fully pursue the field of hydrodynamics, I just really want one of those cups. XD)