THREE DEFINITIONS OF CHARACTER ARC

DRAMATURGY
In dramaturgy terms, a scene is a series of beats with a twist or a change at the end. A sequence is a series of scenes with a bigger change at the end. Acts are a series of sequences with a big change at the end. And ultimately a story is a series of acts with one, big irreversible change (or reversal). Part of that change includes the main character. Character arc is that big change in the climax of the story where a character makes a new choice and reveals his new self. Dramaturgical approaches include Robert McKee, Lajos Egri, Jeff Kitchen, Syd Field.

MYTHOLOGY
In mythological terms, a character arc is a symbolic death (a literal death in American Beauty) in which a character dies to his old self and is resurrected into his new self. This is not like the cheap thrill in a horror film where the monster seems to die only to come back to life umpteen times. This is how a character hits rock bottom, makes or prepares to make the worst choice of his life and then manages to rise up. (Related mythological approaches are found in Joseph Campbell, Chris Vogler, and Stuart Voytilla)

PSYCHOLOGY
In psychological terms a character arc is when a character achieves Integration (Freud) or Individuation (Jung), i.e., when the character makes a choice using his entire self—not just a wounded or limited portion—and becomes whole. It’s when a character sheds his defense mechanism(s) and acts from his core being—not from fear, pain or worse. Related psychological readings include Michael Hauge, Bruno Bettelheim’s Uses of Enchantment, Freud, Jung.

For instance, when analyzing the climax of a script, dramaturgy tells us where to look for the ultimate change in the character, mythology tells us how that that climactic scene might look and how to accentuate it, and psychology shows us what the change is.