The script creates the plot and the actor creates the story. In other words, the script creates the “what” and the actor creates the “why”. What is happening versus why it is happening. The why is the part that moves the audience. The less you let the overall story talk your character out of her or his own story the stronger and more vivid your character will be on camera.
Actors are taught to create “the moment before”. On camera, to create the character’s story create “the scene before” and carry that into the current scene. You create what your character was feeling in the previous scene, and let that be the subtext of the scene you are currently playing. This will create the character’s story within the overall story. The result will be a three dimensional performance on camera.
For example, a scene is between a boss and an employee. In the scene, the boss is firing the employee. The employee is protesting, and the boss is holding the company line. Imagine that the boss’ most recent scene was with her or his own superiors, and they were forcing your character’s boss to fire your character, and it was breaking your character’s boss’ heart because she or he cares about your character. Let the boss be emotionally stuck in the previous scene with her or his superiors while in the current scene the boss is forced to fire your character.
Want to use the same cinematic weapon to create comedy? Let the boss’ most recent past encounter have been a seductive flirtation with a coworker. Now let the boss be stuck in the seductive flirtation while in the current scene the employee being fired is protesting and the boss’ words are defending the company.