The sweet spot of a ledge is the furthest point from the edge at which a character can still grab the edge. This is normally in reference to a recovery move, such as up B. This distance varies for different characters, with some characters, such as Captain Falcon and Ganondorf in Melee, being unable to sweetspot. Other characters, such as Dr. Mario, can sweetspot from farther away.
In Brawl and Super Smash Bros. for Nintendo 3DS/WiiU, 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 Corkscrew, can auto-sweetspot the ledge.
Players try to sweet spot the edge 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, sweet-spotters are vulnerable to edge-hogging.