Stephen King echoed Faulkner's comment when he stated: Kill your darlings, kill your darlings, even when it breaks your egocentric little scribbler's heart, kill your darlings.
Now, what exactly does kill your darlings mean? To me, it has two interpretations. The first being to actually take out a character. Keeping the same characters through the entire story makes for a predictable tale and nobody hates predictable more than avid mystery readers. So shake it up. Say goodbye to one or two of your darlings. Yes, it's sad. It'll hurt but it'll spice up the story.
And think about it - if you're so attached to little Susie or Bog Mo that killing them off seems so repugnant, so I can't bring myself to do it, know this - your readers will feel the pain too. It stirs the pot and that's a good thing. If you're a fan of The Game of Thrones, you've witnessed the beheading of Eduard Stark, the double murder of two main characters during a wedding feast, or the satisfying killing of King Joffery . George R.R. Martin spares no one and he does it to change the dynamic of the story and impact the remaining characters.
Ready to do it? Find the right moment in your plot - the time when it'll stir the pot and produce a new direction in your story. I wouldn't put any character off-limits, including the offing of a central character like Martin did. But remember the cardinal rule - never, ever do it unless it advances the plot. Otherwise you're only creating chaos. Chaotic writing irritates readers. Irritated readers put chaotic books aside, never to open the pages again.
The second interpretation is the killing off of your most beloved pieces of writing. That cute witty dialogue between John and Jane or even whole scenes. Not the best ones. If you enjoyed writing them so much, chances are your readers will enjoy them too.
But how would you know what's darling and what's not? Perhaps the characters don't act right or the plot stagnated. Something about a particular paragraph or scene feels off. Narrative or that snappy dialogue just doesn't seem to fit, or the pacing is not right, or a snippet of dialogue doesn't quite seem to fit. Read through the manuscript. If your mind wanders, that passage probably needs to go. Re-write it or toss it.
If you're wavering - should I kill that passage or leave it, you ought to engage a critique partner or an editor. Bottom line is whatever moves the story forward is likely a keeper.