wear two hats指的是“身兼两职”，也就是同时做两份工作或者完成两个任务。

【例句】
They are so shorthanded in the school that the schoolmaster has to wear two hats.
学校缺少人手，校长只好身兼两职。

I’m wearing two hats tonight—parent and teacher.
我今晚身兼两职——既是家长又是老师。