How do capacitors store energy?
Electrostatic potential between the plates.
When the capacitor is charged it stores positive charge on one plate and negative charge on the other. There are repulsive electrostatic forces between the like charges on the plates. There is therefore the potential for the charges to do work on each other. No work can be done until a circuit is connected between the plates because there is nowhere for the charges to move to. When the circuit is connected charges are forced off of the plates toward the other plate.