The main elements of a story that serve dramatic functions are the characters themselves. The BBC states that minor characters in MacBeth serve a dramatic function of motivating the major characters throughout the story.
https://www.reference.com/art-literature/define-dramatic-function-495072bf0a09cac1
Supporting the major character are one or more secondary or minor characters. whose function is partly to illuminate the major characters. Minor characters are often static or. unchanging: they remain the same from the beginning of a work to the end.
http://www.unm.edu/~hookster/Elements%20of%20Fiction.pdf
happen and what actually happens (situational irony) or between what a character believes or. says and what the reader understands to be true (dramatic irony). Plot, the action element in fiction, is the arrangement of events that make up a story.
http://www.unm.edu/~hookster/Elements%20of%20Fiction.pdf
Even the Bible has elements that offer dramatic functions, according to Cambridge Journals. The slave girl Rhoda's dramatic function in the Book of Acts is to heighten the realism in Luke's storytelling.
https://www.reference.com/art-literature/define-dramatic-function-495072bf0a09cac1
Irony (from Ancient Greek εἰρωνεία (eirōneía), meaning dissimulation, feigned ignorance), in its broadest sense, is a rhetorical device, literary technique, or event in which what appears, on the surface, to be the case, differs radically from what is actually the case.
https://en.wikipedia.org/wiki/Irony
Dramatic Purpose or Significance. Definition: A term which is applied to the use that a scene or a speech (or part of a speech) may have in fulfilling a specific objective. A specific scene or speech in the play may be said to have a dramatic purpose of significance if it achieves one or more of the following:  Establish setting.  Characterization of a main character.
http://hrsbstaff.ednet.ns.ca/twatson/dramatic_purpose_or_significance.htm
Q: I have a basic question: What is meant by a 'character's dramatic function?'. A: A character's dramatic function describes the structural reason your character is in a story. In Dramatica, the storyform contains the underlying structural and dynamic components of a story's dramatics. Part of those dramatics are the character elements (e.g. pursue, avoid, temptation, etc.). Assigning character elements to a character in the Overall Story throughline gives that character a dramatic function, meaning that character needs to be in the story because it fulfills a structural requirement.
http://dramatica.com/questions/what-is-a-characters-dramatic-function
On this aspect, the Oxford English Dictionary (OED) has also: A condition of affairs or events of a character opposite to what was, or might naturally be, expected; a contradictory outcome of events as if in mockery of the promise and fitness of things. (In French, ironie du sort).
https://en.wikipedia.org/wiki/Irony
How do I define dramatic function? A: A dramatic function is the reason for various elements of literature and drama to exist within a story, according to Indiana University-Purdue University Fort Wayne (IPFW). Every element in a story serves as a way to move the plot along.
https://www.reference.com/art-literature/define-dramatic-function-495072bf0a09cac1
The American Heritage Dictionary's secondary meaning for irony: incongruity between what might be expected and what actually occurs. This sense, however, is not synonymous with incongruous but merely a definition of dramatic or situational irony. It is often included in definitions of irony not only that incongruity is present but also that the incongruity must reveal some aspect of human vanity or folly.
https://en.wikipedia.org/wiki/Irony
what is meant by the dramatic function of a character
Meant by the dramatic function of a character is the structural reason your character is in a story.