Chemical potential energy or bond energy is the energy released by chemical reactions. We often hear that energy is "stored" in chemical bonds and released when the bonds break, but this really isn't the case. Compounds form because it is energetically favorable for that to happen, meaning that it results in a lower energy, more stable configuration. The formation of chemical bonds releases energy and the breaking of bonds absorbs energy.
When a chemical reaction is exothermic, meaning it releases energy, the bonds that were broken absorbed less energy than what was released by the formation of new bonds. Some reactions are endothermic - they result in more energy being absorbed than released. When we say that a chemical reaction produces energy we're referring to the net change in energy, not just the energy change associated withe the breaking of chemical bonds.