So, since I've been going on about characterization and narrative structure for the last few posts, I figured it's time to tell you one of the most basic things that you can use to test your story to see if it meets all the requirements of having an actual narrative and characters, rather than a bunch of things that happen and props for them to happen to.
This is the acid test for writing.
It's very simple, really: remove something from your story. Does this substantially change the narrative? If so, then congratulations. That part of your story has passed the acid test. It is integral to the plot, and needs to be there.
The exact details of how to apply the acid test can vary, of course. When applying it to characters, you can just remove them from the story, but that will change how things go in most cases. That really only shows whether or not your character is a plot device. To tell whether or not your character is a character, have them switch roles or dialogue with another character. Are they essentially interchangeable? Can you swap out dialogue between the two characters and not be able to tell the difference? Are the two characters able to fulfill the same roles in the story without any changes to their personalities? If they can, then they have failed the acid test. They're interchangeable and therefore not distinct characters.
When applying the acid test to events within the story, just remove the occurrence entirely. Do your characters get attacked by bandits? Have the bandit attack never occur. Does the story have to be changed substantially in order to accommodate this alteration? If not, then the event is unnecessary, and has failed the acid test.
This is, of course, just a rule of thumb. It is neither the best nor the most reliable way to test your story. For example, the acid test only really applies to the main cast, and only reliably so to rounded characters. Flat characters, due to their lack of depth, can fulfill almost any role easily and still have a point in the story. Certain characters might be designed to be simple plot devices. The fact that two characters are similar does not automatically mean that they're unnecessary to the story. And so on. Events within the story might not be strictly necessary to advance the plot, but might provide our characters with a little bit more development or the like.
Ultimately, only you can decide whether or not a character or event is necessary for your story. The acid test is only meant to give you a rule-of-thumb means of judging things offhand. It's a tool, to be used as needed and discarded when not.