A tether recovery is any recovery that connects a character to the nearest available ledge. Link, Samus, Lucas, Zero Suit Samus, Olimar, Ivysaur, and Toon Link all have tether recoveries, either as their Up specials or by attempting to grab while in the air. Tethers have a blinding weakness in the form that they will be incapable of grappling a ledge unless it is completely unoccupied. Unless tether characters are careful, they may easily succumb to being edge-hogged. In Brawl, a tether character can only grapple the edge successfully three times without landing on the stage. Any subsequent attempts after this will automatically fail.
However, despite this weakness, tethers can be used as great edge-hogging mechanisms themselves in that you can freely hang momentarily as an enemy approaches the ledge, then hit A to be carried there and abuse the invincibility frames gained.