Districts
Districts are subdivisions of beaver communities. They extend from District Centers in all directions until they reach a District Gate. The boundaries of a District can be extended by Paths but only to 70 tiles (08/May/2022 gameplay), with this being increased or decreased by elevation. The current boundary of a District can be seen by clicking the District Center and following the Path Line until its termination.
A building must be within and connected to a District by a Path for workers to use it. Workers will go outside of a District to gather materials, such as a Lumberjack to cut trees, a Scavenger to salvage metal, or a Gatherer to pick Berries, so long as the resource is within the area of their Flag. Builders will also construct buildings outside of their District so long as there is a Path to it. This means it is possible to construct a building, connect to it by Path, and still not be able to use it if it is too far from the District Center.
Path Network
Each District has its own Path Network, originating from the District Center and extending out to all paths connected to it. District Path Networks cannot cross each other, requiring a District Gate to separate them.
When a District Center is selected, a Path Line will extend from it indicating the extent of the District's boundary. As the line continues, it will change color from green to red, red indicating you are reaching the limit of what that District Center can reach. Eventually the line will end, even if a path continues, indicating the District's limit.
Establishing a New District
In order to establish a new District, a new District Center must be built which can be done for free and without a builder. There can only be one District Center in any given District, so the planned expansion must be segregated from any existing Districts before building the District Center, either by District Gates or by simply removing linked paths.
Resource Division
Each District has its own Population, 
Well-Being and Resource pool. Needs satisfied in one District will not automatically be satisfied in another. Likewise available resources in one District will not be usable by another. Workers will not cross District Gates to work but can be Migrated via their District Center. Resources can be shared between Districts by using the Distribution Post and Drop-off Point to create Trade Routes.
As of 9/23/2021, it is possible to circumvent some of these restrictions. If a Storage Building is built between two districts, the resources inside of it can be freely shared by removing the path to it from one District and reconnecting it to another.