As an analogy, a capacitor can be compared to an elastic membrane across a pipe. Pressure (voltage) causes it to stretch and store some flow / current, proportional to the pressure / voltage.
If the voltage / pressure reduces, the membrane starts to spring back to its neutral position, and forces some of the stored flow / current back.
A capacitor "membrane" is a fixed insulating layer rather than elastic and the storage is electrostatic, but they are equivalent functionally.