The basis on which towns were labelled as 'Black and White' is **Racial Discrimination**.

**Racial Discrimination:**
Racial discrimination played a significant role in labelling towns as 'Black and White'. This discrimination was based on the racial segregation policies that were prevalent in the United States, particularly in the southern states, during the period of segregation.

**White Towns:**
- White towns were predominantly inhabited by white Americans.
- These towns were often characterized by better infrastructure, access to resources, and opportunities.
- White residents enjoyed privileges and advantages denied to Black residents.

**Black Towns:**
- Black towns, on the other hand, were predominantly inhabited by African Americans.
- These towns often had poorer infrastructure, limited access to resources, and fewer opportunities for residents.
- Black residents faced discrimination and segregation in various aspects of life, including housing, education, employment, and public services.

**Impact of Racial Discrimination:**
- Racial discrimination led to the creation of separate Black and White communities, perpetuating segregation and inequality.
- Black residents were systematically disadvantaged and marginalized, facing barriers to social mobility and economic advancement.

In conclusion, the labelling of towns as 'Black and White' was a result of racial discrimination that was deeply ingrained in the societal norms and policies of the time. This discrimination had far-reaching consequences for the residents of these towns, perpetuating inequality and segregation based on race.