"Last time aliens invaded all they did was force the most intelligent of us to pair off and mate continuously... Oh, yes..."
A specific kind of Applied Phlebotinum often used in Fanfics to get two characters who have little motivation to have sex to do so.
In the most traditional use of this trope, aliens kidnap the characters and require them to have sex for scientific study or experimental purpose. The trope's meaning widened to include any case where an external force contrives, orders or forces the characters to have sex for its own purpose. The trope is parodied as often as used straight.
A Shipping trope. Often used in Slash Fic, or with Crack Pairings of characters who hate each other. May lead to MPreg justified by alien technology.
A variety of Deus Sex Machina, and an extreme case of Kissing Under the Influence. Compare with Mate or Die.