The Ancestral Hall 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 Ancestral Hall is a huge help if you're building a wide empire. With added Production toward Settlers and a free Builder in newly-founded cities, you'll be able to expand your empire and develop your land with ease. The Government Plaza is not always prioritized in the early game compared to other districts like Campuses, Commercial Hubs, and Harbors; however, if you want to pick the Ancestral Hall as your Tier 1 government building, you need to get it as soon as possible. There is nothing worse than getting this building so late that there's no open space nearby to settle.
The Ancestral Hall has great synergy with Magnus' Provision title, as it allows you to spam Settlers without adversely affecting the city's growth. The Colonization policy is another point of synergy; the Production bonus from the policy stacks with the bonus from the building.
Remember that, unlike most other Government Plaza buildings, the Production bonus granted by this building is not empire-wide - only the city with the Government Plaza gains this 50% Production bonus towards Settlers. However, any new settlement (after this building is completed) will start with a free Builder, regardless of where the Settler is trained. The effect that grants a free Builder is bound to this building, not to the Settler, so if a Settler is trained before the completion of the Ancestral Hall, but founds a city after its completion, the new city still starts with a Builder. On the other hand, if a city is founded when the Ancestral Hall is pillaged, no free Builder will be granted regardless of where and when the Settler was trained.
The Ancestral Hall is a building associated with veneration of ancestors, and the best examples of these come to us from China (although variants on the concept have been built elsewhere throughout history). They exist to serve as a place where the living might demonstrate their respect and honor for the previous generations in their lineage, and to conduct important familial ceremonies, such as marriage and funerals.
As the seat of a lineage, they serve as an important locus in the identity of a family. No matter how far away a family may move, they know that they can return to their ancestral hall and reconnect in an important way to their place of origin. This grounding of identity is a source of strength for these people, making them feel like part of an unbroken chain of human effort and achievement.