"Mercy fuck" is slang in American English. If you have sex with someone just out of kindness or pity for their sexual desperation, you have given them a mercy fuck.
It can be an act of pure altruism, or one of royal condescension. One might get a mercy fuck from a friend for being sad, or ugly, or a virgin, or broken-hearted.
One might use the term to insult someone, as in "He's never going to get laid unless someone mercy-fucks him." Or if someone says "My god! Why would you ever go out with that dweeb!", you might reply "It was a mercy fuck," signifying your position above the mercy-fuckee in the hierarchy of sexual desirability.
It brings up some interesting thoughts; it is a fairly benign way to talk about motivations for a sexual encounter, unlike the usual terms where sex is a thing of conquest or objectification, rather than of empathy.