The Blue (蒼 Ao, localized as Azure) is an almighty power deep within the Boundary.
The Blue of the Abyss (深淵の蒼 Shin'en no Ao, localized as the Azure Abyss and Abyss of the Azure) is the place to where the souls return and sleep. It is the final destination of the soul. A necessary step in resetting and rebuilding the world, is sending all the souls of that world back to the Blue.
Arakune is obsessed with finding the energy of the Blue. He hunts down those that exude the same energy or traces of the Grimoire. Coming into contact with the energy is what caused his form to degrade into the monster that he is. According to him, Litchi Faye Ling is being devoured by the energy as well, and that she should resist the temptation to embrace it any further.
Arakune once simplified the Blue to "bioenergy" and "memories", while according to comments dropped by Relius and Izanami, it is mostly made out of "life" and "souls". It is also described as "The light from which the world sprang". Roy himself specifies it as a place where memory of the man's remembrances are kept, the place where "records" are gathered.
The perfect Contact Prime Field, did not need the Blue Grimoire to become Kusanagi, because she already inherited the Blue.
Es is the Conciliator (調停者 Chōteisha) and the guardian of the Blue Gate (蒼の門 Ao no Mon), and by the will of the Blue she guides the Protector of the Blue (蒼の守護者 Ao no Shugosha, localized as Azure Guardian), it means Ragna, to the gate.