This phrase means, literally: “try again.”
In Shakespeare’s play, Henry V, King Henry uses this phrase to encourage his soldiers, who are launching an attack through a breach in the walls of French Harfleur. His words are, “Once more unto the breach, dear friends, once more; / Or close the wall up with our English dead.”
Here “breach” means gap, and “unto” is into. Used in our everyday lives, the expression implies that, whatever battle we are fighting, we should have the courage to try again.
That’s easy to say when one is still under the covers, the only thought in mind a cup of fresh coffee.
However, we could try harder and “burn the midnight oil.”
To “burn the midnight oil” means, in modern slang, pulling an all-nighter.
Originally, one worked late into the night using the light of an oil lamp or a candle. Most of us today are fortunate enough to have electric lighting.
The first person known to have referred to “the midnight oil” in print was the English author Francis Quarles, who used it in Emblemes in1635.
At that time people used a specific verb for working late by candlelight: elucubrate. Henry Cockeram defined it thus in his The English dictionarie, or an interpreter of hard English words, 1623.
Obviously, that word is no longer of much use. And, though no one I know actually works by candlelight or an oil lamp now, the phrase “burning the midnight oil” is still in everyday use.
As an aside, in the 80s and 90s there was a very popular Australian band called Midnight Oil, whose biggest hit was “Beds Are Burning.”