Welcome to English in a Minute. Sometimes American English is confusing and hard to understand. Like? Burn the midnight oil.
Everybody knows American burn a lot of oil. But is there a special oil that they burn in the middle of the night? I have a big exam tomorrow. Are you prepared?
No, not at all. I have to burn the midnight oil. I need to do well on this exam. Americans are not burning special oil reserved for the middle of the night.
They are just staying up very late. This actually makes sense if you think of a candle or a lantern and you have a lot of work to do that may take you all night. This is a phrase everybody will understand.