You can think of bond enthalpy as a measure of stability (potential energy). So, when we see a bond enthalpy for an O = O as 495 kj/mol, we are saying that when 2 monatomic oxygen atoms approach each other and form that double bond, 495 kj of energy are relased per mole. The two oxygen atoms are much more stable in that arrangement than they would be if they were individual atoms floating about in proximity to each other. That same amount of energy would have to be put into the double bond to break it, and separate those oxygen atoms. Bond breaking is always endothermic, bond formation is always exothermic. We can get an approximation of the enthalpy change for the reaction overall by comparing the total energy needed to break bonds (reactants) to the total energy we get back from bond formation (products).
ΔHrxn = Bonds Broken - Bonds Formed
