The Reservation of Separate Amenities Act, passed in 1952, gave formal legal protection to the racial segregation of public space that was already widespread throughout South Africa at the time. The dominant Afrikaaner minority of South Africa (decedents of Dutch settlers) were committed to maintaining a white supremacist system that denied the indigenous people of South Africa access to most of their historic land and full rights through the apartheid system. Apartheid (from "apart" + "hood") built on the historic colonial conditions that developed under British colonial rule and intensified them as South Africa shifted from British to Afrikaaner rule.
The Reservation of Separate Amenities Act specifically applied to public vehicles, services, and spaces. Following a court ruling arguing that segregated facilities needed to be equal (similar to the US doctrine of "separate but equal" racial segregation) the government passed the Reservation of Separate Amenities Act to explicitly protect segregation without any facade of equal facilities.
Thus, we can see the act as having a few major effects: first, allowing whites to move through public space without encountering members of South Africa's indigenous population. By decreasing contact, the apartheid regime was able to make it harder to build solidarity across racial lines, allow white residents to more easily ignore the mass poverty apartheid inflicted on South Africa's black residents. Additionally, the policy allow white residents to have less crowded and higher quality public services/spaces, since black residents were denied access. Further, the segregation of public space supported residential segregation and the general apartheid model of seeking to create a white-only society, keeping the indigenous population confined to living in poor, overcrowded conditions in small pieces of land that the ruling white majority was not interested in.