Hearts serve as the energy mechanism behind Shop Heroes and are required to successfully suggest or demand a surcharge on items sold to visiting heroes. Selling heroes exactly what they requested will add to your hearts total while modifying their request or the price at which it was requested will deplete your hearts total.
You can increase your hearts total by upgrading the counter and purchasing decorative furniture within the store. Racks and city boosts from investing in the Town Hall will also help with replenishing your hearts quickly.