"I'm so tired," he said, yawning and stretching his arms.

stretching 是动词 stretch 的现在分词形式。stretch 的意思是"伸展、拉长"，指通过伸直或拉长身体部位来放松肌肉的动作。在这里 stretching his arms 表示"伸展手臂"的动作。