The Warlord's Throne is a Tier 1 government building in Civilization VI: Rise and Fall. It is built in the Government Plaza district and requires a Tier 1 government (Autocracy, Classical Republic, or Oligarchy).
The Warlord's Throne is a great building to have if you plan on waging lots of wars and taking over your enemies' cities. Quite self-explanatory, anytime you plan to go down the path of a warmonger, you should pick this building. The bonus does get triggered by capturing City-states and Free Cities.
The English word "Warlord" is of relatively modern coinage (it first appears in the 1850s) but the concept of the military leader of a civilization with outsized power is an ancient one. Analogous terms such as "Dux Bellorum" in Latin (the origin of the noble title "duke"), or junfa in Chinese during the 20th Century, have appeared independently multiple times throughout history, inevitably linked to the idea of a military leader whose actual power exceeds that of his notional rulers. Although the king may reign, the warlord often rules.
A successful warlord is one who can translate success on the battlefield into political capital, and so consequently many successful warlords throughout history can be found erecting monuments to their glory (such as Trajan's column), modifying existing monuments (such as Cleopatra's Needle, whose history is as interesting as its name is misleading), bringing along hagiographers (such as those with Alexander the Great), or surrounding themselves with their own courts of followers (such as Cao Cao, founder of the Kingdom of Wei). Sometimes this means creating a building where the warlord can plan both military and political campaigns and confer with their trusted advisers -- solely for the good of the state, of course.