About the technique

The up and down fingerstyle is achieved by up and down pickings of 2 pairs of fingers.  
First there is the pair index and middle, then we have middle and ring finger .
This is the main technique for the pair index finger and middle finger:
1 middle finger up picking, 2 index finger up picking, 3 index finger down picking.

This is the main technique for the pair middle finger and ring finger:
1 ring finger up picking, 2 middle finger up picking, 3 middle finger down picking.

It consists of a movement of 3 which goes up, up, down. 
As stated this is the Main technique but at times when playing  with the pair index/middle finger also the middle finger can go down picking too and same for the pair middle/ring finger, also the ring finger can go down picking too

Playing with all 3 fingers together  while switching pair of fingers

As stated this is the Main technique, so at times when playing  with the pair index/middle finger also the middle finger can go down picking too and same for the pair middle/ring finger, also the ring finger can go down picking too.
The up, up, down explained above works best when playing fast single notes. 

There are ways to practice and the first exercise is to dedicate time to each pair of fingers.
With both pair of fingers play up and down strokes on scales, arpeggios and just anything.

What are the benefits? As the nail surface above is different from that below, for each finger you are going to have 2 slightly different tones (up tone and down tone) and this makes it particularly interesting when you play jazz.
Super fast fingerstyle single note playing.
The up and down fingerstyle is mainly meant for single notes playing, it is a skill that together with other techniques, including the only up strokes single notes playing, adds a new vehicle for guitarists bound to the destination of making music.
This is an upgrading breakthrough innovation for the fingerstyle guitar playing.