A reservoir capacitor is a capacitor that is used to smooth the pulsating DC from an AC rectifier.
The above diagram shows reservoir performance from a near zero impedance source, such as a mains supply. As the rectifier voltage increases, it charges the capacitor and also supplies current to the load. At the end of the quarter cycle, the capacitor is charged to its peak value Vm of the rectifier voltage. Following this, the rectifier voltage starts to decrease as it enters the next quarter cycle. This initiates the discharge of the capacitor through the load.
These circuits are very frequently fed from transformers, and have significant resistance. Transformer resistance modifies the reservoir capacitor waveform, changes the peak voltage, and introduces regulation issues.