Your pets inventory can hold four types of items: furniture, clothes, food, and fish.
Furniture: This includes wallpaper and flooring, furniture, and other household items sold in the furniture store. These items are used to decorate your pets home and some are even interactive. HPS currently releases three new room themes each Friday. Each room theme contains 10+ items to the set, which can be bought and collected separately from the furniture store.
Themed Rooms that have been released so far can be viewed on the happylabs blogs page here.