An inductor carrying current $I$ stores energy $U = \frac{1}{2}LI^2$ in its magnetic field. This is analogous to $U = \frac{1}{2}CV^2$ for a capacitor. The energy is stored in the magnetic field itself, with energy density $u = B^2/(2\mu_0)$ (compare: electric field energy density $u_E = \varepsilon_0 E^2/2$). For a solenoid: $U = \frac{1}{2}LI^2 = \frac{B^2}{2\mu_0} \times Al$ (total energy = energy density $\times$ volume). When the current is switched off, the stored energy must go somewhere — it can cause sparks across switches (back-EMF).