After their fight, he cried his eyes out in his room.

cried 是动词 cry 的过去式，意思是"哭泣"。 his 是形容词性物主代词，意思是"他的"。 eyes 是名词 eye 的复数形式，意思是"眼睛"。 out 在这里是副词，表示"完全地、彻底地"。 cried his eyes out 是一个固定表达，字面意思是"把眼睛都哭出来了"，形容哭得非常伤心、痛哭流涕的样子。