Official response from Adriel Hampton
Precinct numbers are numerical codes unique to each of the precincts within the state. Precinct codes are the names associated with those numbers. The list of precincts you have created for your nation can be found at in your control panel under People > Precincts.
NationBuilder expects your nation to have distinct precinct codes for each precinct. Precincts can also have distinct names for each precinct.
If you are searching for the voters in a specific precinct, you can search for either the name of the precinct or the code assosciated with that name. You are not able to search for both at the same time.
For most states, the name and the code each indicate the same precinct. In some states such as AZ, precincts are defined with a combination of the code and name. If your state uses a name and number combination to indicate distinct precincts, you need to create precinct names for each precinct that contain both the name and the number (you can do this by concatenating the name and code field in Excel).
For example M0002 Apache. M is the county code, 0002 is the precinct code, and Apache is the name of the precinct. Each of the three pieces is needed to define the precinct, so precincts in AZ need to be defined as precinct names in NationBuilder instead of as precinct codes.