Nervousness or anxiety experienced when performing or speaking in front of an audience.
I got stage fright at my first recital.
He is the type who easily gets stage fright.
緊張 is general nervousness or tension, while 舞台負け specifically refers to stage fright.
Compound of 舞台 (stage) and 負け (losing, being overwhelmed), literally 'being overwhelmed by the stage'.