Keepers are elves with minds that are practically impenetrable.
When something is too important to write down, the Council or another organization gives the secret to a Keeper to remember and protect. They are mostly Telepaths. It is the Keepers' job to remember things.
At the beginning of Book 1: Keeper of the Lost Cities, Quinlin thought that Sophie Foster is, or had the potential to be, a Keeper due to the fact that the Black Swan made her with an impenetrable mind, which is the ideal for keepers. Sophie and Fitz later discuss this, talking about how either Sophie or Fitz could become Keepers because of their near-impenetrable minds.
The opposite of a Keeper is their partner, a Probe.