The design of full wave rectifier is as shown below.
The capacitor in the initial part is uncharged. That means no voltage difference exists between the plates of the capacitor. So when the voltage is turned on, the charging of the capacitor happens immediately.
During this conduction period, the capacitor charges to the maximum value of the input supply voltage. The capacitor stores a maximum charge exactly at the quarter positive half cycle in the waveform. At this point, the supply voltage is equal to the capacitor voltage.
When the AC voltage starts decreasing and becomes less than the capacitor voltage, then the capacitor starts slowly discharging. So the capacitor does not get enough time to completely discharged. Before the complete discharge of the capacitor happens, the charging again takes place. So only half or more than half of the capacitor charge get discharged.
The pulsating Direct Current (DC) produced by the full wave rectifier contains both AC and DC components. Capacitor allows the AC components and blocks the DC components of the current. So the capacitor component removes the ac ripple.