We know that bond formation releases energy and bond break absorbs energy. I still don't figure out why ATP hydrolysis (that breaks a bond between oxygen and phosphorous) releases energy, and it releases a LOT.
ATP synthesis is actually an endergonic process, hence the need for oxiditative phosphorylation to drive the formation of ATP. Although the P-O bond releases a large amount of energy, the reverse of this process is not occurring in ATP hydrolysis. During hydrolysis, the ATP is broken down into two products, with the addition of water, these products are more thermodynamically stable, so energy is released. Breaking of the P-O bond does require energy, but because more energy released by adding the water in, the overall reaction releases energy. ATP is a thermodynamically unstable molecule (bond breakage releases free energy), but is kinetically stable (bond breakage has a high activation energy). I am not too sure what the exact reasons for ATPs hydrolysis being exergonic are, textbooks state it is because the major sources of the free energy associated with the P−O bond dissociation are the relaxation of the electronic repulsion, increased resonance of the products and the stabilisation of the solvation free energies of the relevant species after the hydrolyses. However, this paper (DOI: 10.1021/acs.jpcb.7b00637) claims that the solvation effects upon hydrolysis actually destabilise the products, but I am not sure of the validity of this paper.