In storytelling writing characters with a flat, straight journey in the story doesn't work. Characters who start one way in a story and remain the same at the end aren't interesting. The character arc boiled down is about how the character starts at point A and ends up at point B changed somehow. Even in script writing this transformation is important to create a compelling script.
How do you keep the character arc in mind. I'm going to give you an example from my forthcoming book Body in the Trunk.
Evan Garner -- philandering player whose sexually irresponsible behavior always leads to his downfall. He meets the beautiful and sweet Mia with whom he intends to con and swindle of her stock options. Then he actually falls in love with her for real. And through his first real love experience he is put in a situation where he finally has to grow up to protect and not abandon her. He is redeemed in the end by his desire to finally do the right thing.
So let's break this down.
Point A: Selfish player who doesn't care who he hurts to get what he wants. In telling the story Evan is transformed as he begins to experience a genuine love connection with Mia. It's the first time through their bond and deep connection that he experiences what "love" is really about. In experiencing love for the first time in his life when put to the test, he stays and doesn't run in an effort to protect her even at his own peril.
Point B: He stays with her even though he must make the ultimate personal sacrifice. In showing the audience his willingness to protect his beloved he becomes more likable. The audience feels sympathy toward his plight, and in his redemption he becomes a better man -- a man that is worthy of the heroine's love.
You see how this makes the story more compelling, too. Had Evan stayed unchanged and selfish throughout the audience would know the story's outcome (it would be predictable). But as Evan begins to change the outcome becomes less obvious. And in developing the character the story is developed right along with it. Hence the value and importance of character arcs.