Okay so this is my super fast introduction explanation that doesn't say all the important things:
The Codex are 32 beings who deal with physical laws of Existence, like thermodynamics, entropy, the Pages (complexity levels, a big thing for another time), in Elkepzel's case atoms and molecules, etcetera. Ranks are I believe the precedence of one Codex or another, although it's only intuitive to me so Nimda/Legend can explain it better than I can.

And this is David's not as fast full explanation that does say all the important things but not the unimportant things. It's not very long don't worry.
Codex are keepers of laws of physics. They used to be guardians of Triggers, the eight items and eight being that could destroy code, basically what everything is made of. But all the Triggers were destroyed in the war, leaving the thirty two Codex completely free. Each one has a different ability, and all of said abilities require incredible calculation skill on the Codex's part to actually perform his or her ability. Ranks (also called "Levels" and "Priority Ranks") are how the Codex council determines the strength of the Codex in question, and when put directly against the physical law control of another Codex, which will take priority and overtake the other. Rank is based on both the calculation skill of the Codex and the ability itself.