Why After rectification the output is a pulsating DC with ripple that must be smoothed. That is done with a low-pass filter: capacitors in shunt (parallel with the load) store charge and hold the voltage up between peaks, while inductors (chokes) in series oppose changes in current. Together they form the capacitor-input or choke-input filters found in classic supplies.
Watch out Diodes are tempting because they are in the same power supply, but they do the rectifying (converting AC to pulsating DC) that happens before the filter; the transformer changes the voltage ahead of that.
Filter = energy storage: caps hold volts, chokes hold amps. Diodes rectify, transformers transform, C and L filter.