A while back, I took a writing class where the instructor was always telling us to get rid of extra characters in our stories.
If you wrote a scene where a man was out to dinner with his girlfriend and two nieces, he'd tell you that there only needed to be one niece.
If you wrote a scene where a child was being bullied on a school bus, he'd tell you to change the bus to a locker room and get rid of everyone but the child and the bully.
If you wrote a scene that took place in Times Square on New Years Eve, he'd tell you to change the scene to a home in the Midwest where the characters were watching the ball drop on TV.
Do you see the problem here?
Yes, there are people who stay home and watch the ball drop, but those are completely different people than the ones who go to Times Square on New Years Eve. If you change the scene that much, not only do you cut out a few extra people from the background, but you also have to completely rethink your main characters.
Obviously if the scene takes place in the middle of Times Square, not every person in that scene is going to have a speaking part, or get an in depth description in the narrative. But, they have a place in the narrative. If your main character wants to propose to his girlfriend in front of thousands of strangers, that's one of the best places to set your story. You're not going to be able to describe every person's reaction, but you can't pretend that they aren't there.
If you take the bully off the school bus and into the locker room you lose the embarrassment factor. Of course the child being bullied is still going to feel awful, and be embarrassed, but if the bullying isn't happening in public, it's a much different scene. On the school bus, there's opportunity for other kids to stand up for him, or join the bully. In the locker room, the victim is entirely alone, unless you force another character to walk through the door.
So how do you know when you need to cut a character?
Think about how much the scene would change if there were fewer characters in it. Think about how your characters would act with less people around. If the scene would still work, if your characters would act the same way no matter who was around, then sure, get rid of the second niece, take the bully off the school bus.
Only cut characters from your narrative when you're positive they're superfluous and the scene will work better because of it.