A Pivot Respin allows Samus to fall off a ledge while somersaulting in the opposite direction of the ledge without grabbing the ledge itself. That is, if the lip of the ledge faces left, Samus can fall to the right, and if the lip of the ledge faces right, Samus can fall to the left.
Over the course of a run, the time saved from the extra horizontal speed is significant. This trick should be applied whenever Samus changes direction when falling off of a ledge, especially when it allows clearing another ledge completely.
If Samus is in the middle of a standing fall, she can enter the somersaulting state (or "respin") by pressing B before landing.
Performing a pivot respin results in a spinfall (also known as a trustfall) that allows for cleaner movement while falling through areas with multiple ledges.
When Samus walks off a ledge, she will enter a falling state. In this state:
With correct timing, Samus will not grab the ledge, but will begin somersaulting in the new direction.
This is a variant of the pivot respin that allows Samus to clear the lip of the ledge slightly higher, thus spending more time at the maximum horizontal air speed.
This method has the additional risk that mistiming the B press causes a coyote jump. However, it is slightly faster, and allows Samus to clear some ledges a normal pivot respin does not.
In Artaria, there is a vertical shaft Samus must descend edge before activating the first magma switch (the room is the one just before elevator D-boost). A single pivot respin can, with well-timed stick flicks afterwards, be used to smoothly fall between the platforms without grabbing or standing on any of them. However, this trick is exceptionally difficult.
A similar fall can be accomplished in the room after Water Platform Skip that can be used to skip three ledges on the way to Charge Beam. This weave is quite a bit easier than Gigaweave.
While in the air, Samus moves faster horizontally when somersaulting.