How does a change from ATP TO ADP provide an organism with energy?

you can think of bonds as a form of stored energy, for reasons that has to do with electric orbitals in atoms which is a bit out of the biological context, so the 3rd Phosphate molecule when bonded to the ADP ( Adenosine DiPhosphate ) will increase the " potential energy " of the new formed ATP ( Adenosine TriPhosphate ) molecule, and later on the ATP is used to perform a certain task by binding to a receptor, the bond is broken simultaneously with the formation of a new bond on the receptor that will alter its conformation or trigger a certain chemical reaction, the energy needed for this chemical modification on the receptor that will cause a chemical or mechanical action to occur is supplied by the breakdown of the bond between the phosphate groups and ATP becomes then ADP+ P

by breaking the bond between one of the phosphates it releases energy for the system to use.