In our theatre classes we often talk about how an interesting scene involves key moments in a character's life. The audience wants to see characters grow, change, make decisions and sometimes fail. And characters must be different at the end of the play from when they started at the beginning: changes have to happen.
In addition, during a key scene, how a character uses the space gives lots of clues as to where they are emotionally in their character journey. As an actor, you should explore dynamic changes in a scene. Find moments that inspire you to move, cross the stage, or change your position (sitting, standing up, etc). Not only is this visually interesting for the audience, it can help you as an actor express what your character is feeling at that moment.
Another important element of a scene is the distance that separates you from the other actors / characters on the stage. So, in a scene with an interesting power dynamic, getting in the other character's personal space can be a bold action that tells the audience, who has the power right now. Characters that stay still while other characters move around the stage also command attention and come across as authority figures.
Physical contact, eye contact (or avoiding someone's gaze) and physical reactions are also all very useful tools to show an audience how your character feels about the other characters on stage.
In general, use the rehearsal time to explore! Try new things every time you rehearse a scene. Once you've memorized your lines, feel free to try the scene while sitting down, try the scene while invading the other character's space, or try the scene by avoiding eye contact. Some things will feel strange or forced and you won't use them in the final performance, but chances are, you will discover new nuances and interesting moments that you can use in the final show.