After the Russian Revolution of 1917, the underdeveloped countries of Africa and Asia had, for the first time, a potentially strong ally in their struggle against colonialism, which was practiced primarily by West European countries like Britain, France, Portugal and by the Dutch. Until the end of World War II, this support from the USSR was mainly rhetorical, as Russia lacked the means to actively support what became known as "national liberation movements."
After the end of World War II, the European colonial powers were comparatively far weaker than before the war, especially relative to the newly emergent Soviet Union that, with the United States, represented the new global powers. Britain, while unoccupied during the war, had nevertheless suffered extensive damage from German bombing raids and was in serious financial straits. Along with France, the Netherlands, and Portgual, Britain found it increasingly difficult to hold onto its colonies, especially the "jewel in the crown," India.
While the colonial powers were weakened by war, the increasing strength and assertiveness of the Soviet Union provided anti-colonial politicians and militants in the colonies a powerful new ally, both in terms of political support and in terms of military assistance to guerrilla movements. While some colonies remained, notably Angola and Mozambique, both under Portuguese rule, the ability of colonial powers to retain their grip on these territories was seriously weakened. Angola in particular became a major East-West battleground in the proxy wars that pitted movements or governments supported by the United States against those supported by the Soviet Union.
An important U.S. ally in these struggles was the Republic of South Africa. Unfortunately, South Africa was ruled by a small minority government dominated by Afrikaneers of Dutch and German heritage. This govenment instituted a government system known as "apartheid," which was intended to prevent majority Black rule from developing by using force to keep blacks limited to small, desperately poor areas of the country while being heavily reliant on that underclass for labor.
Ultimately, the apartheid regime in South Africa fell because, unlike most countries with seriously bad human rights conditions, an international consensus developed during the 1980s against apartheid. The scale of economic and political sanctions imposed on the govenment of South Africa became untenable, and the white regime relinquished power.
The collapse of the Soviet Union, which had supported the African National Congress, had little bearing on developments in South Africa. The ANC was already the dominant emerging political force in South Africa, and had never had to be as reliant on Soviet military assistance as many other insurgencies. In fact, but for the scale of economic sanctions imposed by the West against South Africa, the apartheid regime would not have fallen, at least for many more years.
The Soviet Union had placed a high priority on supporting national liberation movements. By the time it ceased to exist, colonialism had ended (excluding limited examples like the Falkland Islands and French territories in the Pacific).