This type of regulation is designed when the circuit you're dealing with requires extreme regulation. Such a demanding system would be a preamplifier circuit or some types of VCO oscillators for instance where utmost stability is required to achieve best results. Bad regulation may introduce noise in the preamp stage which usually carries the distortion for futher amplification by the power stage. In oscillators it may cause the frequency to drift which is also an undesirable effect.
About the How? The left one uses a constant current source and some filtration to achieve the astonishing -127dB attenuation which will decrease a 1V ripple down to 500nV. The circuit on the right is a similar topology but instead of Constant Current Source, a bootstrap is used to achieve similar effect with the same dampening factor. I personally recommend the one on the left. The right one is very hard to tweak and requires these exact components to work properly while not having any dissimilarities in parameters to the other one.
