A building is a permanent structure that can be built in a city to provide a bonus. In Civilization VI buildings are less centralized, as some can be built in the City Center, but most are built in a specific district. In this way, during war, the enemy may Pillage districts and disable some of the buildings in a city without actually conquering it. It also means that in Gathering Storm disasters may devastate whole groups of buildings, when they hit the district they're situated in.
Constructing buildings can be accelerated via Industrial City-States. The Capital gains a +2 Production bonus from every such City-State where you have at least 1 Envoy. All other cities which have an Industrial Zone (including the Capital, if it has one) will gain +2 Production bonus from every such City-State where you have 3 Envoys, and another +2 Production if you have 6 Envoys. In Rise and Fall, however, these two bonuses are awarded only if the Industrial Zone contains a Workshop and a Factory (respectively).
Note that, once constructed, a Building cannot be removed from a city! Unlike in Civilization V, Buildings cannot be sold.
As in all Civilization games, all buildings need to meet specific requirements before they can be built in a city. These are:
Technologies or Civics - You need to research/develop a specific technology or civic to unlock each building. The only exception, as usual, is the Monument, which is available right from the start.
District - In Civilization VI most buildings can only be built within a certain district. Thus, you need to first build a specific district in a city before you can actually build certain buildings.
Other buildings - All buildings belonging to a certain district are organized in a hierarchical way. More advanced buildings require the more basic ones; the University, for example, requires a Library. The only exceptions are they buildings in the City Center, which can be built freely (except for the Walls upgrades, which need to be built in order: Ancient, then Medieval, and finally Renaissance).
Religious Belief - a group of buildings (namely, all Tier 3 buildings of the Holy Site) each require the city to have the particular Religion as its Majority religion.
Mutually exclusive buildings - There are some district buildings which cannot reside together with another specific building in the same district (and thus in the same city). For example, you cannot have the Barracks and the Stable at the same time - you need to choose only one.
In Rise and Fall,Government Plaza buildings also require you to adopt a Tier I, II or III Government.
Every building in a city enhances its usefulness in some way. Most of the time this means increasing certain yields, such as Food or Culture, but it may also mean extra Amenities, Housing, or even extra defense for the city. But Civilization VI and its innovative territory use system adds some unique possibilities, such as for an inland city to access oceantiles via the Harbor, and be able to build ships there!
Buildings in Specialty districts (such as the Commercial Hub or the Campus) also provide slots where Citizens may work as Specialists, producing rare yields independently of what terrain there is nearby. This is especially useful in the early game, when producing stats like Science and Culture is more difficult. Note that, unlike Civilization V, Specialists don't contribute to Great People generation, but that hardly matters because buildings themselves already contribute to that, without the need to assign Specialists to work in them!
Another interesting feature is some building effects now extend not only to the parent city, but also to all other cities within a certain range, as is the case with the Production bonus of the Factory, or the Amenities bonus of the Zoo. Buildings of this type can only be found in the Industrial Zone and Entertainment Complex, so it is beneficial to build those districts in locations within 6 tiles of as many City Centers as possible.
Finally, most of the slots for Great Works, Relics and Artifacts are found within buildings.