Minor characters play essential roles in narratives as they help to advance both the plot and support the themes as well as assist in the development of the main character.
In F. Scott Fitzgerald's famous novel, The Great Gatsby, the minor characters of Myrtle and George Wilson are truly essential to the creation of conflicts that underscore themes and propel the sequence of events. For instance, as the mistress of one of the main characters, Tom Buchanan, Myrtle is the cause of conflicts between Tom and his wife Daisy; later, in the narrative she is struck by a car driven by Daisy and killed. Her death triggers a number of actions and conflicts, one of which is George's killing of the protagonist, Jay Gatsby.
Certainly, the introduction of Fortinbras into the plot of Hamlet is what finally propels the melancholic prince into finally avenging the death of his murdered father, an action requested by King Hamlet's ghost in the first act.
So, without minor characters and their interaction as well as reactions to the main characters, the depth of a narrative will certainly be lacking as fewer external conflicts will exist.
Through their traits, minor characters further the development of themes. Again, using The Great Gatsby as an example, Mrytle Wilson's interactions with Tom demonstrate the hedonism of the Roaring Twenties; also, her death and the callous way in which the Buchanans--"careless people"--make Gatsby their scapegoat demonstrates the theme of the selfishness, irresponsibility, and materialism of the Jazz Age, all themes of Fitzgerald's novel.
In Julius Caesar, for instance, Lepidus, who is one of the triumvirs with Marc Antony, formed as the enemies of Brutus and Cassius after a civil war breaks out following the assassination of Caesar. When Antony callously dispenses with him by sacrificing him for political reasons, this character's outcome furthers the central theme of Ambition.
Often a minor character acts as a foil to a main character. That is, by his juxtaposition with the main character, the reader, viewer/listener will notice certain traits about the main character as they are brought out by the contrast between the characters. In Hamlet, for instance, the foil character Fortinbras, who is willing to sacrifice his life for a tract of land, a battle that is more about honor, Hamlet is moved to act in defense of his murdered father. In Mary Shelley's Frankenstein, Henry Clerval is also a foil: A gentle man of letters, rather than science, Clerval is loyal and loving toward his friend, but Victor Frankenstein causes his own friend's death.
Indeed, the development of minor characters is often very important to narratives of different genres. Certainly, meaningful character development is intrinsic to a good narrative.