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 quicksand.
First, build up forward momentum by either sprinting or rolling. Then pause using the gear menu. While paused, begin and continue to hold target (ZL) and a control stick position known as ESS Down. ESS refers to holding the control stick barely outside of its deadzone in some direction (So ESS Down is barely outside of the deadzone in the Down direction). If you go into your control stick calibration settings (System Settings > Controllers and Sensors > Calibrate Control Sticks > press left stick) this is the what ESS Down position will generally look like. Note that this position is precise and can be frustrating to hit consistently. Once you feel that you're holding ZL and ESS Down, unpause the game and Link will begin brakesliding.
If you attempt to brakeslide but Link just stands still, you weren't holding far down enough. If Link moves but his speed decreases very quickly, you were holding too far down. You can use those cues to help gauge what an optimal ESS Down position feels like to you. The closer you are to the deadzone without actually being in the deadzone, the faster Link will move during his brakeslide.
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 quicksand, 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.