ATP contains a series of three negatively charged phosphate groups. When hydrolysis of ATP occurs, one of the phosphate groups, bearing two negative charges, is allowed to separate from ADP, containing the other two negative charges. Just as work would be needed to push negative charges together, potential energy decreases when they are separated. (It is not so simple, though, there is also an additional internal energy decrease because of increased resonance stabilization in ADP, solvent effects, as well as the crucial effects of coordination with magnesium ions. It's not so simple!)
In summary, defamiliarize your perceptions. Think about ATP as a system of charges in molecular form. The three negatively charged phosphate groups are like a coiled spring. The electrostatic potential energy of like charges are held together in ATP, kinetically but not thermodynamically stable. Imagine pushing it all together. You are imagining the high internal energy and enthalpy of ATP. Combine this idea with a sense of the probability of the phosphate being available, just randomly showing up to make ATP from ADP, and you are getting a sense of the free energy. Phosphoryl transfer potential is the 'force that drive the green fuse through the flower' in the immortal words of the poet Dylan Thomas.
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