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.
Dropping such a character from the story without reassigning its function(s) would cause holes in the story's dramatic argument.