The Equistore is the place where you can buy the following items for your horses: Food and treats, bedding material, halters, and tack for specific disciplines.
In the future, all these items will play a more central role for the game-play. For now, food and bedding items are not yet required to care for your horses, and tack doesn't seem to affect competition scores yet. Also, currently not all treats are working as they should. However, halters are working as intended and add a score boost in conformation shows.