"Codex" here is a very broad term to designate collective or individual knowledge. It can be either owned by a character, an organization, or a culture.
It can be a map revealing astral objects, a story with useful information for yourself or another character in the game (it unlocks dialogue paths or missions), it can be secrets that can alter the reputation of a character or an organization, and last but not least it can be theoretical sciences, technologies, and designs.
While all the backend programming is done, I'll only talk here about the first batch of codex entries, for sciences and technologies.
About 70 technologies and theoretical knowledge were added, constituting a full basic tech tree from a primitive era to the spacefaring one.
Codex entries have bonuses and modifiers, which can increase the max possible dev on a tile :
They can allow the construction of buildings, spaceship designs, spaceship modules design, affect the population growth rate, and the administrative capacity.
Some entries also can affect an entire culture or organization, by providing bonus/malus on cohesion or reputation, and can even alter the ethics.
This is the total bonus of an advanced civilisation :
Codex entries can be found when exploring the galaxy, and it is planned to make it a tradable commodity.