Apartheid was the South African system of complete racial segregation. The system officially began in 1948 and ended in 1994.
Racial segregation and discrimination did not start in South Africa in 1948. Aspects of what would become the apartheid system were in place long before that time. For example, laws had already taken away the rights of black South Africans to be members of parliament or to own land outside of specified areas of the country. In 1948, however, the government committed itself to a more formal program of apartheid. This happened because many blacks had come to the cities during WWII and it had become clear that existing laws did not segregate them fully enough to satisfy the majority of whites. The existing system also did not do enough (in their minds) to ensure white dominance of the economy. The National Party ran its campaign that year on the platform of setting up apartheid. They won the election and apartheid was imposed.
Apartheid was not imposed all at once in 1948. Instead, laws continued to be passed in the succeeding years that fleshed out the system. For example, it was only after 1948 that blacks were denied the vote and that the government tried to force more blacks to live in “Bantustans” that were set up as segregated homelands for different black ethnic groups.
Apartheid came under more and more fire from the international community as time went on. South Africa was subjected to things like bans on its participation in various international sports. There was a strong movement in the United States in the late 1980s and early 1990s that urged American investors (particularly colleges) to divest from South Africa as long as it practiced apartheid. South Africa’s white ruling class, in the form of the National Party, finally gave in in 1994, ending apartheid and introducing democracy.
So, insofar as apartheid started in any given year, it is said to have started in 1948.