Molecules tend to go from high energy forms to low energy forms. Low energy forms are more stable. Small molecules tend to be lower energy and more stable than large molecules. When molecules break down into lower energy forms, energy is released, because the total amount of energy is conserved. Some of the energy that's released is used to build the high energy bond in ATP, which is the bond between the third phosphate and the second phosphate. ATP is made from ADP + phosphate. Enzymes are needed to transfer the energy from the broken bonds to ATP. Otherwise the energy from the broken bonds would be lost as heat.

Every day we use an amount of ATP comparable to our body weight! This is what Paula Bruice says in her "Organic Chemistry" book.

Molecules are also more stable when their electrons are in pairs, and the electrons' orbitals, or 'shells', are full. That's why atoms like nitrogen bond with a 2nd nitrogen atom to make nitrogen gas. Oxygen gas molecules have 2 oxygen atoms, but oxygen gas isn't as stable as nitrogen gas; oxygen gas reacts with many things and oxidizes them.

This website compares chemical energy storage to water at the top of a hill that loses energy as it runs down hill:

This website also has a nice comparison of different elements in the periodic table, explaining how they react to get electron numbers like the inert gases, which react with almost nothing. The inert gases are very stable.

That's a start at answering your question. It's not an easy question to answer.

This is a great question. It's more of a biochemical question, and I'm not a biochemist, but I'll do my best. We biologists often talk about energy being contained in bonds and released when the bonds are broken. What really going on is that some bonds are broken and other bonds are formed.

Think about it this way. Suppose someone tosses your favorite candy toward you. You grab it because you are attracted to it. Atoms are attracted to each other by their opposite charges. Remember that electrons have a negative charge and the protons in the nucleus have positive charges. So the electrons and protons are attracted to each other. They attract each other in the same atom, but also between atoms.

Atoms form molecules with bonds between the atoms when their opposite particles are attracted to each other. (Particles with the same charges repel each other.)

You're not going to just let go of the candy unless you're offered something better. Now suppose that you are shown a twenty dollar bill but can only take it with the same hand that is holding the candy. You would probably drop the candy and grab the 20 because you are more attracted to it.

Stable molecules don't fall apart on their own, but adding a bit of energy may break them apart and allow them to make even stronger bonds. The greater the difference between the weaker bond that is broken and the stronger bond that forms, the more energy is released to do work. Think of this as just dropping one candy for a slightly better one, but throwing the candy if you got to grab a $100 bill.

When we break down food, such as glucose, we break the weak bonds inside the glucose molecule and the atoms form stronger bonds in other molecules. It takes a bit of activation energy to break down the glucose. We'll get a lot of energy out (about 16 times the activation energy) by the time we have broken the glucose down through many steps to get all the atoms in the glucose into H₂O and CO₂ molecules.

ATP (an adenosine with three phosphates) makes a good energy carrier because it is so unstable. When one phosphate breaks off, a lot of energy is available for doing work.

I hope this helps. You may want to study biochemistry to understand this sort of things better.