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Potential energy U = qV for a charge q at potential V. For systems of multiple charges, U = ½Σᵢ qᵢVᵢ (factor of ½ avoids double counting). Energy is required to assemble charges against the field.
From your study of electric potential, you know that the electric potential V at a point in space is the potential energy per unit charge placed there. This gives the simplest formula in this topic: if a charge q sits at a location where the potential is V, its potential energy is U = qV. This is a direct product — no integration required. The sign matters: a positive charge at a positive potential has positive potential energy (it would release energy if allowed to move to lower potential); a positive charge at a negative potential has negative potential energy (it is in a bound configuration).
The subtlety arises with systems of multiple charges: what is the total potential energy stored in an assembly of N charges? You might try summing qᵢVᵢ over all charges, but this double-counts: charge 1's interaction with charge 2 is identical to charge 2's interaction with charge 1, and a naive sum counts each pair twice. The correct result is U = ½Σᵢ qᵢVᵢ, where Vᵢ is the total potential at the location of charge i due to all other charges. The factor of ½ is the fix for double-counting, and it appears throughout electrostatics whenever you move from pairwise interactions to a self-consistent sum.
Think of assembling the system step by step, bringing charges in from infinity one at a time. The first charge costs no energy (no existing field to work against). The second charge must be brought in against the field of the first, costing U₁₂ = kq₁q₂/r₁₂. The third charge must be brought in against the fields of both previous charges, costing U₁₃ + U₂₃. The total is the sum over all unique pairs — which is exactly what the ½Σᵢ qᵢVᵢ formula computes. This assembly energy equals the energy stored in the electric field throughout all space, a deep connection that becomes explicit when you study energy density of the electric field.
The practical consequence is that energy is required to assemble like charges and is released when opposite charges are brought together. The binding energy of charge distributions — from capacitors (charges on two plates held at a potential difference) to atomic electron shells — is computed from exactly this accounting. For a capacitor, the stored energy U = ½QV = ½CV² emerges directly from this framework: the ½ has the same origin as the ½ in the charge assembly formula.