Character arc

A character arc is the internal change a story forces on a character — the movement from what they believe at the start to what events have made them believe by the end.

The Fantasy Fiction Formula puts it bluntly: the whole point of a plot is to force the protagonist to change. The plot is not the story's purpose, it is the pressure — and the arc is what the pressure does.

The most reliable shape is built on a false belief. The character enters holding something to be true (I can only rely on myself), the plot punishes that belief again and again, and the climax puts them somewhere they must abandon it to win, or keep it and lose. That is why an arc and a throughline are not the same thing: the throughline is the want, the arc is what the want costs.

The change also has to be earned. A happy ending a reader will believe is one the character paid for; readers forgive almost anything except a transformation that arrives because the last chapter needed one.

Not every character arcs. A flat-arc protagonist holds a true belief and changes the world around them instead, which is how a series hero can stay recognisably himself for twelve books while everyone he meets does the changing.