According to the dictionary, a story is a "narrative, either true or fictitious, in prose or verse that is designed to interest, amuse or instruct a listener or reader." It is essentially a series of events told from a point of view and where the audience also plays a role in its function. A story cannot be a story without these key ingredients, though the variety of these ingredients are what makes the world of story a vast and beautiful one.
When "story" is broken down for study by writers and readers of story, the elements are often described as follows: Point-Of-View (Narrator), Character, and Plot. Now, there is much more to the study of narrative that I'm not including here, like theme and symbolism and use of language, but I want to focus on these three items because they are what remains essential to story. Without any one of the three, Point-Of-View, Character(s) or Plot, the story or the root of the narrative begins to fall apart.
In order for the listener or reader to understand the story being told, they have to be introduced to the character or characters by the narrator. It is also the narrator's responsibility to build the world that the characters live in and possibly drop some helpful hints to the audience as to why things are the way they are in this story's world. So the writer's first task is to determine the best narrative voice that will tell the story while they write. Why must it be the best? Because to fall short in this aspect allows for misunderstanding and misinterpretation, which will inevitably disengage the audience from the story.
Some writers will argue that story is all about the character. That everything should be subservient to the character - particularly a character who is also the narrator - and that the plot should follow. Characters help to set the mood of the story, especially if they have a heavy role as a narrator, and they also help the reader to understand and become part of the story as a sort of empathetic viewer. This is the great magic of story and indeed the part that most readers fall in love with in the beginning. Characters can actually transform our view of our own world in this way. However, if the character does nothing but chat with other characters and show the reader around the elaborate set of their "world," the story always falls flat. Things must happen in order to move the narrative and thereby give the story meaning.
This is where plot comes into play. Stories that lack plot, or rather fall short in its development, are often very poor in other aspects like narrative voice and character development. Plot is the driving force behind story. It is the reason why the characters have a story to begin with - otherwise they're just little cardboard cut-outs bouncing along a painted background (probably not even bouncing for that matter). Without plot, a character has no where to go and nothing to do. Which doesn't sound like a very exciting thing to read. Plot therefore gives the character a goal to accomplish, somewhere where they have to end up in the end. Plot can be simple or complicated, borrowed or blended, but it should always have a beginning, middle and an end. It doesn't have to start at the true beginning and it doesn't have to follow any rules. It's life - things happen.
The most beautiful and meaningful stories have solid roots in these three aspects of narrative. They do not get caught up in their own clever use of language or descriptions of character or scenery. All of that is just extra bits added on to entice a demographic to pick up a book - not to tell a story. A good story is universal in its understanding, and a great story will always stand the test of time.