Chanced across this term (by means I never imagined I would). Given the circumstances of the day, it was like telepathic homily on a Sunday morning.
It refers to a practice where writers are get rid of the things they “love the most in (their) writing”. Specifically, to let go of the bits of your writing that you hold so dear to you, but don’t really serve to advance your story in any way. You wanted it to fit, you tried to make it work but alas, there just wasn’t a place in time for it.
A little bit of googling tells me that Sir Arthur Quiller-Couch originally termed it “murder your darlings”. Perhaps too graphic. But perhaps, quite appropriate. To wholeheartedly root for something but have it die by your own hand. Oh hang on, my “oh don’t be so dramatic” light has just come on.