bond enthalpy
Bond enthalpy is the energy it takes to pull apart one particular chemical bond — to break the grip holding two atoms together. Every bond is like a stretched spring locking two atoms in place; snapping it open costs energy, and forming it back releases the same energy. Bond enthalpy puts a number on that cost, measured as the heat needed to break one mole of a given bond in the gas phase.
It gives us a way to estimate the heat of a reaction by simple accounting. Breaking bonds in the reactants always costs energy; making new bonds in the products always gives energy back. Add up the energy spent breaking, subtract the energy regained forming, and the leftover is roughly the reaction's enthalpy. If the new bonds are stronger than the old ones, energy is released and the reaction is exothermic.
This is why burning fuel releases so much heat: weak bonds in fuel and oxygen are traded for the very strong bonds in carbon dioxide and water, and the difference floods out as warmth. Bond enthalpies thus give an intuitive, molecule-level picture of where a reaction's energy comes from.
Breaking one mole of H–H bonds in hydrogen gas takes about 436 kilojoules. The very strong O–H bonds formed when hydrogen burns to water give back even more — which is why the reaction releases heat.
Energy in to break bonds, energy out to form them; the balance is the reaction's heat.
Tabulated bond enthalpies are averages over many molecules, so estimates from them are approximate, not exact — the strength of a C–H bond shifts slightly depending on its surroundings. They also apply strictly to gas-phase species, so they overlook the extra energy of melting, vaporizing, or dissolving. For precise values, use formation enthalpies and Hess's law instead.