I do not know of any law called the “Segregate Amenities Act.” I assume that you are asking about the Separate Amenities Act, which was a law passed in South Africa in 1953. That law, also known as the Reservation of Separate Amenities Act, was passed so that South Africa’s white government could create segregated and unequal facilities without fear that they would be declared illegal by the country’s courts.
Before 1953, segregation already existed in South Africa. However, courts had ruled that the segregated facilities had to be equal to one another. The facilities for whites could not legally be made better than the facilities for blacks and other races. This did not satisfy many white South Africans since their system of apartheid was clearly based on the idea that whites were superior to blacks and other races.
The Separate Amenities Act stated that segregated facilities did not have to be equal. It also allowed the government to completely ban people from public facilities on the basis of their race. It did these things because the white government of South Africa wanted the legal right to segregate non-whites in inferior facilities and /or to exclude them from facilities altogether.