The Falls is a waterfall in Mystic Falls, and is presumably the waterfall from which the town gets its name. It comprises of one big waterfall flowing down a cliff side then a bunch of other smaller waterfalls divided by man-made dividers. There are caves by the Falls, as Elizabeth Forbes mentioned searching them for vampires in You're Undead to Me. There is also a bridge by the Falls, where Elena Gilbert and Stefan Salvatore talked in the Pilot.
The big waterfall may have been present in The Last Day as the waterfall Elena and Stefan walk by on their trip up the mountain. The Falls made a third appearance-- though only in Elena's mind-- in I'm Thinking Of You All The While, when Stefan used his vampire telepathy in order to say his goodbye to Elena after she was put in a suspended-animation sleep spell by Kai Parker, from which she cannot wake until Bonnie dies.