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 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):
I am one, sir, that comes to tell you your daughter and the Moor are now making the beast with two backs.
The origin of the phrase is in French: la bête à deux dos, because it appears in Rabelais' Gargantua and Pantagruel, c. 1532. This was translated into English by Thomas Urquhart and published posthumously around 1693. In contrast, it is believed that Othello was written by Shakespeare in approximately 1603.
In the vigour of his age he married Gargamelle, daughter to the King of the Parpaillons, a jolly pug, and well-mouthed wench. These two did oftentimes do the two-backed beast together, joyfully rubbing and frotting their bacon 'gainst one another.