What exactly the director and the actor needs to do is communicate what it is the character is doing through the story. To do this you start by defining their Objectives.
Main objective or Through-line:
Every character in a story wants something. This may revenge for the death of a loved one, companionship or to solve the mystery of the Matrix. This "want" in acting terms is known as the character "objective". Early on you want to define with the actor what this is.
The main through-line of the character breaks down in exactly the same way as your story breaks down in to scenes and each situation requires a Scene objective. Without a strong purpose to come into a scene, a character has no dramatic reason to be there so you need to make sure the actor has a clear idea of their objective: What do the characters want from each other in that scene? For example Neo from The Matrix wanted to learn the truth to the question "What is the Matrix?" So he has to follow the white rabbit, learn to trust Trinity, escape the Agents etc.
The subjective is the reason why the characters want to attain their objective. The subjective heightens the stakes of a scene, filling the actor with a desperate "need" to find what ever it is they seek. Without the subjective "reason" there is no reason and so the scene lacks drama. Imagine a scene where a boxer is in the ring fighting. His objective is to knock out his opponent but this alone is both boring for the audience to watch and for the actor to play. However if the subjective (the why) is because his newborn baby is dying and the prize money will pay for the life saving operation then everything changes and the stakes of the scene are high. The more they need "it" the more emotion it will evoke in the actor as they try to attain it.
This brings us on to what is known as the "actions". These are what the character has to actually "do" in order to achieve the objective. If you were to break your characters story down in to its smallest moments it would contain a list of verbs: he studies the facts, he asks questions, he spies his enemy, he holds his wife etc. If the actor really commits to these specific actions in order to attain their objective then they have a reason for everything they do, which in turn will ensure the fluency of the physical, emotional, intellectual and aesthetic life of the performance.
To quickly summarize all the above:
The Through-Line – The main objective that your character is pursuing.
The Scene Objective – What your character wants from scene to scene.
Actions – What your character does in order to achieve these objectives.
Subjective – An important reason why the character pursues