Making the beast with two backs is a euphemistic metaphor for two persons engaged in sexual intercourse. It refers to the situation in which a couple—in the missionary position, on their sides, kneeling, or standing—cling to each other as if a single creature, with their backs to the outside.
In English, the expression dates back to at least William Shakespeare's Othello (Act 1, Scene 1, ll. 126–127,):[1]
The earliest known occurrence of the phrase is in Rabelais's Gargantua and Pantagruel (c. 1532) as the phrase la bête à deux dos. Thomas Urquhart translated Gargantua and Pantagruel into English, which was published posthumously around 1693.[2]