By tapping directions on the control stick while being struck by the opponent’s attack, you can subtly nudge the way your fighter flinches. This defensive mechanic is relevant only while attacks are connecting, not when they’ve launched victims away; at the point of launching, that’s when directional influence comes into play.
Hitstun shuffling is most useful against multistage attacks that hold defenders in place for several seconds. This gives the most time to react and the most time to register lots of inputs, causing more shuffling. Examples of attacks that provide a good opportunity to try shuffling are the multi-hit neutral attack combos of Bowser Jr. and Inkling, among others. These types of attacks finish with a flurry of small hits, a dozen or more at a time, which provide a good chance to try shuffling out by rapidly tapping backward. Basically, any multi-hit attack or combo is a candidate for shuffling.
Shuffling occurs in the direction you tap, and more taps are better. Like shield-shifting and directional influence, this is an extremely situational defensive technique, and not something to worry about much at a novice or intermediate level. But when you start looking for every trick you can find in every kind of situation, it can make a difference.