There are several reasons why different covalent bonds have different amounts of stored energy, but one contributory factor is the difference in electronegativity between the atoms being bonded.
When the difference in elecronegativities is high, such as that between hydrogen and oxygen in the water molecule (H-O-H), then the bond energy also tends to be high (about 110 kcal in this case).
If there is no, or little difference in electronegativities between the atoms in a covalent bond, then the bond energy holding them together is lower. A bond between two carbon atoms, for example (C-C) is only 80 kcal. Or between hydrogen and carbon (two atoms with very similar electronegativities) the bond energy is about 98 kcal.
The larger the bond energy, the higher the amount of external energy it will take to pull the atoms apart, and thus the stronger the force holding the atoms together. Molecules, like water, where all the bond energies are high, are very stable molecules and very hard to break apart.
In most, natural, spontaneous chemical reactions, therefore, when molecules with low bond energies crash into one another it does not take much energy to rip them apart. However, when they reform into newer molecules, they tend to form those kinds of molecules that are more stable. These stable molecules have a much larger bond energies holding them together.
In chemical reactions is it easy to get molecular hydrogen to react with molecular oxygen (both molecules held together with lower energy covalent bonds) - all it takes is a spark to get it going!
But when the new molecules form, they consist of hydrogen bonded to oxygen in the form of water. The bond energies in a water molecule are much higher, and thus the molecule is much, much more stable and cannot easily be pulled apart again.