What is the term for an improvement in performance caused by the perception that others are watching?

The answer is social facilitation. It is because the social facilitation affects an individual in a way that they would produce a different effect or actions that they are going to show and display when they are exposed to an audience. It is related above as it says that the improvement of a person's performance because of people watching is trying to depict the meaning of social facilitation in which a person acts differently when shown in the crowd or displayed in the audience. Their actions could either display a good or bad performance depending on their attitude of having other people watch or look at them.