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.
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).
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.
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 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!
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.