For those not into pets - this is a collection/skill challenge, where you have to defeat a group of (NPC) pet tamers, usually geographically grouped, using all pets from only one ability family to win a fight. All Mechanical pets on your team, for example; or all Dragonkin pets.
There's achievements for completing each family against all of the designated tamers, and then an achievement for the whole shebang with, as mentioned, a pet as a reward.
I got Gerald, a charming Magic bird, as a reward.