The Pet Store is a building where you can buy your pets from. At the moment, only cats and dogs may be purchased from the pet store. (Rabbits are purchased from the home store and fish are purchased with real money).
The Pet store is located between the Salon and the Hobby Store (Promotion Store). The time and simoleons it takes to build the pet store depends on how many buildings you've put up before it. You can purchase pets for all your sims. They are quite expensive, depending on the breed and all cost lifestyle points (ranging from 5-80 LP).
This store is attained at level 11 after completing The Mysterious Island quest. This starts 'A Quest for Toddlers' and one of the goals is to build the pet store. It cannot be built before the quest starts.