They are important, but you don't need them (but you have to have an inductor if you do not not use one). You need one, or an inductor, or both because if you did not you would a lot of ripple on the output (a waveform that is jumps between a peak voltage and 0V.
Ideally, bigger the capacitor the better. But real capacitors have parasitic inductance which rises with capacitance. So eventually the inductance is so large it blocks the AC components you want to filter out from even getting into the capacitor (so then it appears on the output as ripple). You want the capacitor to be big enough capacitance, but small enough parasitic series inductance to get the output ripple that you want.
**broken link removed**