A Brake Slide is a trick that allows Link to maintain forward momentum from a roll or sprint without losing stamina. It is the fastest form of movement for a TAS, and is useful in RTA speedruns for traveling quickly through sinksand.
First, build up forward momentum by either sprinting or rolling. During that, immediately switch to holding Z and ever-so-slightly down on the control stick (similar to ESS position). If done correctly, Link should slide forward while maintaining his momentum, but his animation will look like he is slowly backing up. In addition, Link's stamina will not deplete while the Brake Slide is active.
It is easier to do this to extend a roll's momentum, but the easiest way to achieve a Brake Slide is to use the Home Menu to buffer in the Z+ESS down inputs.
As discussed above, Brake Sliding is currently the fastest form of movement, although it is TAS-only. In RTA speedruns, it can be used to move quickly through sinksand, as you can maintain momentum and not use stamina. In particular, a Brake Slide can be used to skip the Temple of Time area after obtaining the Hook Beetle in Lanayru Desert. It can also be used in lieu of an Ampilus shell to cross the sand inside the Stone Cache.