Capacitor smooths out the rectified wave. Simple design with major shortfall; change in load resistance changes current drawn which can change the capacitor requirement.
Top circuit is unfiltered circuit. You can see here how the power supply voltage charges the capacitors by comparing the waveforms between the circuits.
Middle circuit is high (1000 Ohm) load resistance; very low peak to peak voltage.
Bottom circuit is lower (50 Ohm) load resistance; Same capacitor as before but the increased current draw drains the capacitor much faster, resulting in a much greater peak to peak voltage. (There are ways around this too)
