To work late into the night or stay up very late working on something.
This phrase dates to the late 17th century when oil lamps were the primary source of artificial light. 'Midnight oil' literally referred to the lamp oil consumed while working after midnight, making it an expensive and dedicated effort since oil was costly and staying up late was unusual before electric lighting.
Before electric lights, staying up past sunset required significant resources and commitment - oil or candles were expensive, and most people's circadian rhythms were more closely tied to natural light cycles. The phrase captures not just late-night work, but the sacrifice and dedication involved in pursuing knowledge or completing tasks when it was genuinely difficult and costly to do so.
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