To straighten one's back; to sit or stand up straight. Also used figuratively to mean hold one's head high or act with pride/confidence.
授業中は背筋を伸ばして座るようにと言われた。
I was told to sit up straight during class.
彼女は舞台に上がると自然と背筋を伸ばした。
When she went on stage, she naturally straightened her back.
緊張したが、背筋を伸ばして堂々と面接に臨んだ。
I was nervous, but I held my head high and faced the interview confidently.