In a capacitor, energy is stored due to the separation of charges on its plates, with one plate holding excess positive charge and the other excess negative charge. This separation creates an electric field, which can be interpreted as the potential energy being stored either in the charges themselves or in the electric field throughout space. The energy density, which quantifies how energy is distributed in the electric field, is calculated using the formula that integrates the electric field squared over all space. This indicates that energy is primarily concentrated within the capacitor, while fringe fields are often neglected in calculations. The discussion highlights the relationship between charge separation, electric fields, and potential energy in capacitors, providing a foundational understanding of how electric energy is stored.