It's a threat used by the Capitol citizens, particularly President Snow, to intimidate the people of Panem.
Here's what it means:
* "Rue" refers to the young girl who is a tribute from District 11, a farming district known for its poverty.
* "The day" refers to the day of the uprising against the Capitol.
* "Rue the day" means "regret the day" or "curse the day."
In essence, the phrase is a threat to the districts, saying that they will regret ever rebelling against the Capitol. It's a way of reminding them of the power the Capitol holds and the consequences of defying it.
The phrase is significant because it emphasizes the power dynamic between the Capitol and the districts, and how the Capitol uses fear and intimidation to control the population.