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Energy is absorbed to break bonds. Bond-breaking is an endothermic process. Energy is released when new bonds form. Bond-making is an exothermic process. Whether a reaction is endothermic or exothermic depends on the difference between the energy needed to break bonds and the energy released when new bonds form. If more heat energy is released when making the bonds than was taken in when they broke, the reaction is exothermic.
Energy is added to break bonds, so there is your simple answer. Bond energy is the amount of energy it will take to break a bond (ironic, because it sounds like the amount of energy it will take to MAKE a bond, even though it's the opposite).