"To speak is to act. That action sets an objective for us: to instill into others what we see inside ourselves. It is not important that the other person will see or not see the thing you have in mind. Nature and the subconscious may take care of that. Your job is to desire to instill your inner visions in others, and that desire breeds action. It is one thing to appear before a good public, reel off a few ta-ta-ta's and walk off. It is quite another to go out on the stage and act!"
While this may seem like it doesn't have much to do with us as animators and has everything to do with the voice actors, I'd suggest we'd be mistaken if we thought this way. Your character on screen has to communicate through their expressions, gestures and actions the visceral reality of what they are saying. In life we speak in order to open up for others the window into the images and emotions, beliefs and ideas locked within our minds and souls. We speak in order to infect others with this reality.
Do your characters exert this inner reality on the other characters in the scene when they move? Can we feel the energy of their communication? Can we see it in their eyes? Feel it on their face? Sense the effort and energy in their body? Or are they merely flailing limply through a series of prescribed generic motions that have some tangental relevance to the spoken words? The eyeline of the character is powerful if we use it properly. We need to feel the character almost burning through the thickness of others in the scene as they try to infect them with their thoughts and emotions. If the character has that focus in their eyes, if they earnestly play the moment to portray their inner reality through words and action on the other characters in the scene- then we start to walk down a path to some powerful performances. And if we don't take the time to work out what that inner reality even is in our characters, if we don't even know how, we will be crippled in our efforts to create animated performances that breathe real life in them.
Animate from the inside out and play the emotion to the other characters in the scene.