staying up late means staying up late at night. Generally, it refers to being sleepy all night or late at night because of something. From "The Story of Li Cuilian, a Quick-talking Story in Qingping Mountain Hall".

Staying up late is a phenomenon that is often heard or done in modern life. It is a bad habit that harms people's health and can lead to some diseases and reduce efficiency. Staying up late is a bad habit, and it is easy to lack endogenous oxygen.