Why Capacitor use in Rectifier Ckt

"The purpose of the capacitor is to filter the positive alternating voltage into a nice flat DC voltage. The capacitor, and the load impedance, form a lowpass filter that removes the higher frequency components of the positive alternating voltage, and leaves the DC component behind, so you get this:"

To be more simple and precise to understand the capacitance get charged during the upward motion of the rectified wave (two half cycles )and discharge during downward motion of the wave resulting almost constant DC voltage to the output circuit of the rectifier as given in the third figure .

The capacitors are also used in

1. To get DC waveform
2. To improve the power factor
3. To reduce the harmonics

Now most of SMPS are of PFC( Power factor corrected ) power supplies which will load as unity power factor on the system. This is to be in-compliant with IEEE.IEC and EMC standards on power supply.

Please correct me if I am wrong, is it not that capacitor will amplify harmonics?

True,The capacitors tend to amplify the harmonics. But in most of SMPS circuits tuned filter ( tuned for 3rd Harmonics ) are used and consists of inductor and capacitor. this works as pass filter and remove all 3rd harmonics generated by SMPS