A Ledge Recovery Attack is performed when you push either A Button or B Button while hanging on a ledge. Your character attacks and recovers from the ledge at the same time. There are 2-3 different Ledge Recovey attacks for each character.
Some Ledge Recovery attacks only work when your character is under 100% damage. Once your character reaches 100% you will perform a much slower attack that can easily be countered (Sheik's quick slide kick becomes a slow elbow attack).