bond energy
Bond energy is the depth of the valley in the bonding-energy curve: the amount of energy you must pour in to pull two bonded atoms completely apart. If the bond is a stretched spring holding the atoms together, the bond energy is how much work it takes to snap that spring for good. A deep valley is a strong bond; a shallow valley is a weak one. This one number quietly predicts a surprising share of a material's behaviour.
It is usually quoted per mole of bonds in kilojoules per mole, or per bond in electron-volts. The primary bonds are strong: ionic and covalent bonds run from roughly 100 to over 1000 kJ/mol, and metallic bonds from about 100 to 850 kJ/mol. The secondary bonds are feeble by comparison: van der Waals forces are only a few to about 10 kJ/mol and hydrogen bonds up to around 50 kJ/mol. That thousand-fold spread is why the choice of bond type dominates everything downstream.
The reason bond energy earns its own entry is its predictive power. A larger bond energy means a higher melting temperature (more thermal energy needed to shake atoms loose), a higher elastic modulus (stiffer resistance to being pulled off r0), and a smaller coefficient of thermal expansion (a deeper, more symmetric well moves less when heated). So diamond, with enormous covalent bond energy, is famously the stiffest, highest-melting, least-expanding of ordinary solids — while a waxy polymer held together between chains only by weak secondary bonds is soft and melts in your hand.
Sodium chloride's ionic bond energy is about 640 kJ/mol and it melts at 801 degrees C; a typical van der Waals solid is bound by only a few kJ/mol and melts far below room temperature. The ratio of bond energies (hundreds versus a handful) shows up directly as the ratio of melting points.
Bigger bond energy → higher melting point and higher stiffness.
Bond energy sets stiffness and melting, but not strength. Real crystals fail at stresses far below what their bonds could theoretically bear, because defects (especially dislocations) let atoms slip past one another long before every bond has to break at once. Strong bonding and high strength are related but not the same thing.