Why were Africans successful in gaining independence from colonial rule?

There were economic realities and political movements that
contributed to African nations throwing off their colonial masters as
well.

Economically, the two largest empires in Africa by
the post-World War II era, France and Britain, went broke.  England was mostly broke
after World War II, and it was no longer feasible for them to project military power
around the globe, or fight wars of subjugation on the African continent.  France had
suffered economic devastation under Nazi occupation, then fought a protracted and
ultimately losing effort in Indochina, and then an insurgency in Algeria.  Their empire
collapsed as a result, and the influence of both nations was replaced by that of the US
and the USSR.

Politically, Pan-Africanism, a movement to
unite African peoples and erase colonial borders, became more popular in the 1950s and
60s, as did Marxism, which many African supported as a means to address the glaring
economic differences between wealthy colonial masters and the native peoples of that
land.

So it makes sense that 1960 was considered the "Year
of African Independence", as seventeen separate nations declared their
independence.