A character arc is the hero's emotional path.
The character arc is important because it is the emotional ups and downs that help the reader put himself in the hero's shoes.
The emotional intensity is what makes the reader care.
The five types of character arcs can mesh in a story to create subplots, but they are usually found independently in a novel.
1) PERSONALITY MAKE OVER: In the quest, the hero faces his darkest fears. His darkest moment is when the hero realizes he is not up to par and he is ready to give up. He might even try to pass on the burden of the quest to someone else. The hero will have to seek help or concoct something that will make other people really proud of him.
2) CLASH: MAN Vs. MAN: The heroes must become the ally of their enemy or competitor. The heroes learn not to feel threatened by the other competitor, to trust him, open up, expose his weaknesses and become friends. The darkest moment is when the heroes both lose confidence in each other and have to revise their commitment and compromise to become friends.
3) DEFENSE MECHANISM: The hero has developed a coping mechanism to deal with any kind of problem. He is trying to distance himself from unpleasant feelings, thoughts or behavior. However, this mechanism does not work. The hero must find a new way to deal with his situation that works better. Defense mechanisms are unconscious, which means that the hero is not aware of what is really going on in his head. The darkest moment is when the hero realizes he has been lying to himself and he needs to face reality or his fears. He is then at rock bottom and needs a "miracle."
4) LEAP OF FAITH: The hero starts as a solid person who fits well in his life and knows his boundaries. At some point along the way (after an unexpected revelation/ after meeting someone who shows him another way/ after being tempted / after a debilitating accident), he encounters something that upset his beliefs or routine or knowledge (think the orphan who suddenly learns his father was the man next door or the priest who falls in love with the wrong person or the professional skier who falls off a cliff and becomes paralyzed, etc) The darkest moment happens when he almost falls to the other side. He might believe the opposite of what he believed before. (Example, if he believed that all men could be saved, now he might think all men are evil). The hero needs to evolve and live with more shades of gray. He may have to choose between the old ways and the new ones. He might need to overcome fear, resentment, revenge, hatred or temptation.
5) COMING OF AGE OR GROWING UP: The hero starts off with one set of beliefs, but due to circumstances (puberty/ aging/ culture shock or finding the truth about something), he needs to try several other paths. He might come back to the first path and choose another path, and so on and so forth until he comes to term with the changes in his life. The hero is like an emotional yo yo. Every time he makes a step forward, he needs to back up two more steps. Every time he discovers that he has made a mistake, he needs to gather more information and scratch what he thought was solid. The swings can be emotionally intense like blows and can cause the hero to be depressive and feel beaten up. The hero will find his answer or his way after he has explored all the options available.
Pattison, Darcy. "Three types of character arcs."
Phillips, Melanie Anne. "Character arc 101."