A character arc – sometimes called transformation or inner journey – is what happens to the ‘inside’ of the character during the course of your story/novel.
Your character begins with one state of mind. Stuff happens, just like in real life, and – the theory is – the character evolves into a transformed character, one who has learned a lesson or too, is older and maybe wiser as a result of what life (you, the writer of the story) has thrown at him/her.
The character might change, not just in his/her perspective of the outside world, but also in his/her status or perceived role within their world. Or, having been confronted with a challenge, the character might have a wobble and then feel even more secure with his/her original core beliefs.
For characters to ‘work’, their arcs need to resonate with your reader. They shouldn’t be accidental. However you write your story – as a planner or pantser, or a combination of the two – during the editing stage, it’s worth spending time reviewing each character and making sure he/she starts somewhere, goes somewhere and ends up somewhere!
The Internet provides a wealth of background reading on character arcs:
You might decide your character’s arc ahead of time – well done you! – but, while writing, especially if your draft is produced during NaNoWriMo, your character may have ‘gone their own way’.
TIP: When it’s time to edit, check the arc of each character and makes notes in your character sketch.