Okay, I'm going to get all math-ish on you here, but bear with me a moment. And I say this as a person who hated geometry. (I liked algebra because it mimics life--in life we are always trying to solve for the unknown--but that's the subject of a different post...)
In geometry, an arc is the path between two points. It is exactly the same with a character arc. A character arc marks the path between your character at the beginning of the story and your character at the end of the story. The change in the character does not happen all at once, it happens gradually over time, a series of small steps before the final climax when the character is remade into his new and improved self.
Think of a baby chick or a butterfly. It pokes and wriggles, attempting to free itself from the egg or the cocoon, until the very end where it makes a heroic final burst and breaks free. And as any naturalist will tell you, it is hugely detrimental to help the creature break free too early because it is in the actual struggle itself that the chick or butterfly will gain the strength to make that final valiant effort that frees it from it’s old trappings. That pretty much sums up a character's internal journey and arc.
This is actually a good picture of a character arc:
You can see the small, incremental steps, moving things forward and upward as well. Small points on the graph eventually build to a whole new place.
By plotting out your character’s growth toward change (either consciously or instinctively) you create a forward momentum in your story, a sense of true movement. Those small steps build on each other. As a writer, knowing and understanding those changes that have to occur help us to design or shape our scenes so they pack the most punch.
Sometime the small steps will be incredibly subtle, as subtle as a shift in perception by the character, a recognition that there is a problem, or that the best friend doesn't have her best interests at heart, or the first time she ever, even tentatively, told someone no.
The good news? You should have a ton of material now for these baby steps if you've been following along in the plotting discussion.