A work of fiction, whether it's a novel or a short story, is the interweaving of certain elements of storytelling. If, as a writer, you neglect any of the conventional elements of storytelling, the story can fall apart. Readers won't accept it and won't become immersed in the world you've tried to create.
The characters are who the story is about. They react to the events of the plot, and cause it to move along by their actions or lack of action. Characterization -- presenting characters as compelling individuals who drive the story and have a life of their own -- provides your readers with a means of emotional connection to the story. Dialogue, actions and interactions among characters all contribute to characterization.
The setting is where and when the story takes place. It influences the characters in dictating cultural and social customs, by which they must abide. It also dictates the level of technological access that characters and organizations have. In some stories, the setting can be presented as a character in its own right, due to its influence on the world. As with characters, setting should both affect and be affected by the plot in some way.
Conflict is the soul of the story; without it, the characters have no reason to do anything outside the status quo. It is what causes characters to act in response to the events of the story. Not all conflict involves a physical confrontation. Several types exist: Person vs. person; person vs. society; person vs. nature or the supernatural; and person vs. self. The plot can have more than one of these types of conflicts; resolving one can lead to another. For example, Luke Skywalker fighting Darth Vader is a person vs. person conflict. Luke's decision about whether to kill Vader is an example of person vs. self.
Narrative structure is how the story is laid out and told. The simplest narrative structure includes exposition, rising action, climax, falling action and denouement. The exposition phase introduces the characters of the world. The rising action builds the character relationships, conflict and plot until the climax, or the main conflict of the story. After the climax comes the falling action, which resolves the characters' personal conflicts. The denouement, the final phase, resolves any loose plot threads.
The perspective determines from whose point of view the story is told. First-person viewpoint is a character within the story's universe telling the events as he or she witnesses or experiences them. It can be the main character, but it isn't always.
Third-person limited viewpoint occurs with the voice of an outside narrator centering the 'camera' on one single character at a time.
First-person viewpoint provides the reader with the most intimate look at the world and plot through a character's eyes, but requires that you maintain the character's voice constantly. In addition, narrating traumatic experiences in first person can be difficult to write convincingly.
Third-person viewpoint allows you to selectively portray a character's emotions or thoughts. It doesn't limit you to a single character. A recent example of storytelling from multiple viewpoints is the "A Song of Ice and Fire" series, which alternates viewpoints between several main characters.
This is perhaps the most important aspect of storytelling. Plausibility, not to be confused with realism, is the ease with which the reader can accept the events of the story as true. This concept is also called "willing suspension of disbelief," which is an unspoken contract between you, as a writer, and your readers. Your duty is to tell a story and make the reader believe in it. The reader, meanwhile, accepts realities in the story that may not exist normally, as well as characters acting on their own accord, not by the will of an author. Maintaining the story's internal consistency -- the rules you set for the world and the traits you establish for your characters -- is essential. Don't arbitrarily change the rules of your story or characters to make the plot work; e.g., if you establish a character as a combat novice who nearly faints at the sight of blood, don't have him or her impassively cutting a swath through your antagonist's army in the next scene without plausible in-story justification.