First of all, what is an arc? Look at the picture below.
An arc starts from point A, rises, and then falls to end at point B. A character arc does the same thing. It is the character’s transformation from who they are at the beginning of the story to who they will become by the end of the story.
In fiction, a story’s main character (MC) will usually face a conflict that will lead them to the climax of the story. The conflict forces the MC to change in some form or fashion to overcome the conflict and resolve the problem. Let me give you an example.
In Forbidden: Book One of the Sanctorian Series, the MC was sheltered, quiet, and kept to herself. The MC, Lyla, faced many difficult circumstances and had to learn to be independent. Due to the main conflict of the story, she changed from an introverted person who was unsure of herself into a strong female lead. Her personality went from point A, rose to the climax due to the conflict, and ended at point B.
Before you begin to write your character into your story, determine how they currently are and then how you want them to be by the end of your story. This will help you later on when you start to map the plot points for your story.