It is almost impossible to come up with a definitive answer about what causes the widespread and desperate poverty in Africa though many have tried. One good example is to look at the change in GDP per capita between 1960 in Ghana and in South Korea. In one it has gone from a few hundred dollars to well over ten thousand, in the other it has actually decreased but remains in the several hundred dollar range.
Africa does not lack for natural resources, in many areas there are in fact very rich deposits of various ores, opportunities for large-scale agriculture, etc.
Some experts point to the poor governance that appears to be a fact of life, kleptocracies, oligarchies, constant revolutions and unrest that serve to create great instability and incredible income inequality.
There are also historical factors that people point to including the damage done by colonization and its after-effects, interference from foreign powers, and the effects of the slave trade.