Walk-Brass - The Dwemer's method of Ascension by Collaboration, the Numidium.
Crystal-Like-Law - Has something to do with "Dracochrysalis", which I'm not too clear on.
Snow-Throat - I tend to lean towered the idea that the Snow-Throat is the throat of the world, and it was made a tower in the ancient heroes' banishment of Alduin.
Orichalc - Unknown, though it was on Yokuda.
Green-Sap - Falinesti, though still unsure in the purpose.
White-Gold - Harnesses creatia in order to mold the world to the wishes of the Ayleids.
Direnni - Auri-El's spaceship in which the convention stabilized Mundus.
Red - The Red Mountain in which Lorkhan's heart was thrown after his death.
Khajiit & Lunar Lattice - Debatable on whether this is a tower or not. It also stabilizes Mundus, keeping Daedra and such out.
So, any clarity on the purpose of the towers?