Most, if not all, of your main characters should have some sort of arc, but let’s focus on the protagonist, because that’s who your story is about, and who should have the most dramatic arc.
What is an arc? It’s how a character changes from beginning to end. Stories are usually about a protag’s journey through a set of circumstances that are so powerful that they change him/her in some deep and meaningful way. In Lawrence of Arabia, Lawrence starts with a passion to avoid bloodshed; later, he comes to enjoy killing. In Casablanca, Rick steadfastly refuses to stick his neck out for anyone, yet by the end he risks his life and gives up the woman he loves in order to help the resistance.
The character arc is really what’s at the heart of a good story. What it takes to move the character from point A to point B is the story. If the character doesn’t change, you have no story.
Likewise, if you have other characters who have a more dramatic arc than your protag, they will overshadow the protag. And perhaps it’s really their story and you’ve chosen the wrong protag?
There are some famous characters who never arc. James Bond, for instance, never really changes from beginning to end. The same is true for many well-known detectives like Sherlock Holmes. That is one reason I’ve never warmed up to mystery novels. I think they’re boring. If the situation the protag battles is not somehow life-changing, then why bother? If it doesn’t affect them enough to change them in some meaningful way, why should it mean anything to me, the reader?
There is one gay mystery writer, whom I will not name, who writes a series of books, all with the same characters who never change. I’ve read several, and though he writes beautiful prose, the stories are dead boring. The protag solves the puzzle and that’s it. His protag always stands outside the story looking in, not really involved and has no person stake in the outcome.
Yet, I’ve read several mysteries where the detective does have a huge personal stake, where s/he is pulled into a life-threatening position and goes through an arc while solving the mystery. So it can be done, and it makes for a much better, IMHO, read.
Most readers want someone who is involved, who has a huge personal stake in the outcome, so much so that it changes how they see and interact with the world.
Character transformation is critical. Readers want goodness and justice to triumph, but we also want the characters to figure something out about themselves, become something they were not at the beginning (hopefully something that makes them a more complete person.)
I know some very talent writers who first determine how they want their main characters to be at the end of their story, then they make them exactly the opposite at the beginning, and try to figure out what must happen to change them so dramatically. Scrooge is the classic example of this. It took three ghosts and some hair-raising insights to turn him from a miserable miser into a generous and joyous person. But he arced from totally opposite poles within the span of the story.
These changes are internal, and to understand how your protag changes, you must have a very clear and detailed idea of their internal makeup at each point of your story. That means knowing your protag inside and out, and how each different adventure affects him/her. For me, that means creating comprehensive character profiles, not only for my protag, but for all my main characters. That takes work, but then, nobody ever said writing was easy.