it literally means "go to bed earlier". But the way it gets used in Chinese as a show of concern for some one or, as a way of saying "good night", is probably more similar to "get some rest", "get some sleep" or "I'll let you turn in"

can also say " don't stay up too late" ————別熬夜！ （早點兒睡！）

have an early night

go to bed earlier

thank you ~~~