It stores charge. A capacitor in its simplest form is two plates separated by a distance so that they don't touch. When you connect a capacitor to a voltage source, the electrons collect on one plate. The negative charge of the plate repels electrons on the other plate and causes current to flow on the other side of the capacitor. However, the plate can only store a certain amount of charge (limited by the voltage of the source) and once the other plate attains an equal net positive charge, eventually the voltage on the other side of the circuit dies out. The charge that is built up on the plate is a form of stored energy, so you could say the capacitor stores energy, but the energy is in the form of charge.
This is at least the way I got it explained to me in my Intro to EE class.