For now these stones, called Flawless-Battlestones, will only upgrade your pet to a rare quality. Later on after patch 5.1 Blizzard will enable stones to upgrade your pet to an epic quality. Stones will also work on wild (caught) and non-wild (TCG, vendor, quest, achievement, etc.) pets.
The one thing to watch out for is that these stones come in two flavors: a general purpose stone, and a family specific stone. Family specific means that the stone will only upgrade a pet of the family that's specified on it, for instance aquatic or undead. General stones will work on every pet family type.
This stone system should really make it quite a bit more advantageous to use non-rare pets initially. Quite the nice little upgrade!
Mists of Pandaria is here! The level cap has been raised to 90, many players have returned to Azeroth, and pet battles are taking the world by storm. Keep an eye out for all of the latest news, and check out our comprehensive guide to Mists of Pandaria for everything you'll ever need to know.