Toys are items that can benefit you both during battle and in the shop. They are separate from Pets and Food and are placed off to the right of the team during the shop phase and under the right-most friendly pet during battle. Only 1 Toy can be in use at any given time - note that this does NOT apply to Hard Mode Toys and therefore both a friendly Toy and a Hard Mode Toy can be active at the same time.
In the Puppy Pack, Toys can only be obtained through buying certain certain pets (listed below in addition to the Toys). All Toys Pets will provide an option between 1 Toy that activates when it breaks (all Toys break after 2 turns) and 1-2 Toys that activate at the start of battle.
Toys have Tiers just like Pets and will have the same tier as the Pet they're summoned from. Toys with higher tier will have priority over lower tier Toys, e.g., An Air Palm Tree ( Tier 6) will activate before a Foam Sword ( Tier 4) and potentially protect a low health Pet before it takes damage from the Foam Sword. Toys can also be higher level depending on the level of the Pet that they come from. Higher level Toys have better effects, following similar power scaling rules to Pets.
Some Pets will have synergies with the Toys, like the Flying Squirrel, which will resummon Toys after they break. Keep in mind that these Pets only work with friendly Toys and will not interact with Hard Mode Toys in any way. See Toy Pets for a full list of Pets that summon and synergise with friendly Toys.
The Unicorn Pack is also home to Pets with Toy summoning abilities, these pets have different triggers for summoning their toys and don't follow many rules as to how many toys summoned or what their effects are. These Toy Pets are a lot less reliant on synergy and often have differing levels of usefulness or drawbacks - use with caution!