Edge sweet spot
The edge sweet spot of a ledge is the furthest point from the edge of a platform at which a character can still grab the edge. This is normally in reference to a recovery move such as an up special move. This distance varies for different characters and each type of recovery move, with some recovery moves having large edge sweet-spots, while others cannot sweetspot at all. Notable recovery moves that cannot edge-sweetspot are Captain Falcon and Ganondorf's up specials in Melee, along with Little Mac's Rising Uppercut and Cloud's Climhazzard (if he is not under Limit Break status).
In Super Smash Bros. Brawl, there are auto-sweetspot specials that allow certain characters to cancel the animation for grabbing the ledge and then can sweetspot the ledge at any direction the character looks. However, not all specials, like Aether, can auto-sweetspot the ledge.
Players try to edge sweet spot when recovering to make edge-guarding more difficult, and therefore guard breaking easier. Sweet spotting avoids most ground attacks by recovering too low to be hit, and if they are hit it makes ledge teching much easier. It also offers the standard advantages of grabbing a ledge such as invincibility frames. However, edge sweet spotters are vulnerable to edge-hogging (ledge trumping in Smash 4).