Games of this sort have been called by this name since at least the late sixteenth century. The game was also played in colonial America.
The first participant rests their hands on knees and bends over, which is called giving a back. The next player places hands on the first's back and leaps over by straddling legs wide apart on each side. On landing he stoops down and a third leaps over the first and second, and the fourth over all others successively. When all the players are stooping, the last in the line begins leaping over all the others in turn. The number of participants is not fixed.
The French version of this game is called saute-mouton (literally "leapsheep"), and the Romanian is called capra ("mounting rack" or "goat"). In India it is known as "Aar Ghodi Ki Par Ghodi" (meaning "horseleap"). In Italy the game is called "la cavallina" (i.e. "small or baby female horse"). In Dutch it is called "bockspringen" (literally "goatjumping"; a 'bock' is a male goat) or "haasje-over" (literally "hare-over").
In the Korean and Japanese versions (말뚝박기 lit. "piledriving" and 馬跳び うまとび umatobi, lit. "horseleap", respectively), one player 'leaps' over the backs of the other players who stoop close enough to form a continuous line, attempting to cause the line to collapse under the weight of the riders.
Media related to Leapfrog at Wikimedia Commons