(coexisting on another dimensional plane)
This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
A battle royale was a fight between many combatants until only one survivor remained standing.
On Terra, the throne world of the Terran Empire, the battle royale concluded a ten-day pageant, which itself marked the official end of the Imperial grieving period for a recently deceased Emperor. At the end of the battle royale, the emperor's successor would be named.
In an article from Carl's edition of The Star Dispatch, this event was referenced in a paragraph describing the ceremonies held on Terra in the aftermath of Emperor Philippa Georgiou's death in the 2250s. (DIS: "Terra Firma, Part 2")