Murder Your Darlings (or sometimes Kill Your Darlings) is a phrase used in editing—particularly self-editing. The idea is that a writer may have some aspect of a story, typically a scene, that she is irrationally attached to. The editing process needs to be merciless though—if a scene does not work to serve the greater story, no matter how awesome it is it needs to be cut. A good writer has the ability to murder her darlings.
Common editing victims include Narm and Purple Prose, though many tropes from the Bad Writing Index could apply. And remember writers, it's never bad to write these kinds of text—the creative impulse should always be followed—leaving them untouched by editing is the sin. And if they need to be excised form the story altogether, perhaps they can serve as the seed that your next story grows around.
This phrase is the source of the movie title Kill Your Darlings.
Not to be confused with Kill the Ones You Love .