http://www.fiestafan.com/forums/showthread.php?t=18205
^Please read, pets are on second post I believe. And also in-game guide is L.
Affinity on pets are similar to affinity for your stats and will affect stat growth accordingly. Example: Unda affinity pets will have added HP bonus every level up while Pyra affinity pets will have added Int bonus. Erda will add to defense, accuracy, and so on.