"Empire Day" is a noun used primarily in British English. It refers to a special day that was celebrated each year on May 24th, to honor the birthday of Queen Victoria, who was the queen of the United Kingdom from 1837 to 1901. This day was also meant to celebrate the British Empire and its colonies.
To summarize, "Empire Day" is a historical term used to refer to a day that celebrated Queen Victoria's birthday and the British Empire.