Demise of the darlings

If you have any involvement with writing communities, I can just about guarantee that you've heard the advice "kill your darlings" trotted out, for good or ill. It's the sort of thing people tend to have a lot of opinions about, myself included.

Frustratingly, though, it's also a concept that (like many other pieces of writing advice) seems to be widely misunderstood, based on the many inconsistent ways that people interpret the idea. To some, killing your darlings is about avoiding getting so emotionally attached to your scenes that you can't cut them out if needed. To others, it's a warning not to be self-indulgent. Other people still rebel against killing your darlings because why would you cut things out just because they bring you joy? There are even some particularly uninformed writers (so I hear) who haven't had the concept explained and assume that it's to do with killing off beloved characters for emotional drama.

So with all of these conflicting perceptions out there crashing into one another, how can we understand the idea of killing your darlings in a genuinely useful way? Why might we want to do it, or not, and how does this contribute to making stories better?