'The Under' refers to the sprawling underground of Jhoutai, particularly its Korum and ruins.
While the surface of Jhoutai is an ecological wonder of innumerable species and vast landscapes, the Under boasts more land and more biodiversity. In many ways, there is more to the under than there is to the surface, but due to its hostility it is largely unmapped.
In a purely logical, factual sense, I know that the Korum is, on average about five kilometers thick. That's counting the submerged sections.
The cities of the Procession, long abandoned after the bloodbath of the Sazashi Revolution, have grown to revile visitors. The same cities which once welcomed life now reject it like a scorned lover. Instead, their halls are host only to the creatures which live down there--to which they have become as accomodating as they were to the Verin.