The economist has an interesting article  linking to this paper trying to work out why it is that Africa is so poor . If you're deeply interested in why so muich of Africa is so depressingly poor then you might well read both pieces.
The general answer is institutions of course. But then the general answer to long term growth is indeed institutions so that's really no great surprise. Africa has no great shortage of the usual things that everyone says is necessary for growth. There's land, water, people, minerals, natural resources, what's missing is the structure that allows these to be melded together into the creation of ever greater value. There's some fairly dry comments in the paper on this:
The first-generation literature argued that a major source of growth failures was the intervention of African rulers in their countries’ economies for largely political purposes. Indeed, one of the main purposes of the many structural adjustment reform programmes implemented in the 1980s and 1990s was to limit the capacity of African rulers and ruling parties to interfere in their economies in order to capture rents with which to reward supporters.
They also note that at least something seems to have been working since the late 90s for the economic growth rates of the continent have risen very strongly. I would blame that neoliberalism, globalisation and the Washington Consensus for that myself.
But behind all of this, and the worrying about whether it will last, I find something immensely cheering. For they make very clear and plain that the current levels of poverty in Africa are nothing unusual in historical terms. The $750 GDP per capita levels of some of the poorer countries are roughly the same as those of the North Sea (ie, Holland and GB) in the late middle ages. The $2,500 or so of South Africa is near the same as those North Sea economies before the industrial revolution really got going around 1800. Something that I find hugely, wonderfully cheering.
For what it shows us is that we didn't become rich by stealing what they had: we were just as poor then as they are now. It means that wealth is something that is built, not taken. And further, that it having been done once is extremely good evidence that it can be done again.
We also have good evidence that it doesn't have to take 300 years. China in 1978 had GDP per capita around and about the same as England in 1600. 35 years later China's GDP is about what GB's was in 1950. It is possible to do this, for places to run through the industrial revolution at warp speed and make, by any rational historical or current world standard, people rich in just one generation.
We can even make a pretty good stab at defining what will do it too: those decent insitutions conducive to grwoth seems to be necessary. One set of which is described in that Washington Consensus. Add in the pixie dust of globalisation and neoliberalism and we do seem to be getting there.