First off, Africa is not a country, it is a continent. Additionally, most people do not understand just how big Africa is. It is not a homogenous place. Here's a visual that gives an idea of the size of Africa
The causes of its poverty are manifold. Africa had slavery for hundreds of years, but African slavery was really a system of cheap labor. Slavery in Africa did not remove talent and skills, it just relocated them to a different region in Africa. When Europeans arrived, they removed millions of Africans, causing a massive loss of skills and talent. The argument that Africans are lazier than Europeans is also dubious. One of the reasons that Africans were used as slaves in the America's was because they were used to hard, agricultural labor. It must also be noted that when Europeans arrived in Africa they greatly harmed indigenous technological development. The region were most slaves came from were from west Africa, which before Europeans intervened was developing productive textile industries. The importation of European cloth destroyed those nascent industries. The slave trade (as well as elephant tusks) was seen as an investment by Africans. In exchange for bringing slaves they could get guns, which enabled them to get more slaves and elephant tusks. This diverted African economies from industries such as agriculture and manufacturing towards slave trading and elephant hunting.
When Europeans colonized Africa, they were not concerned with developing manufacturing in Africa. Europeans developed extractive industries and infrastructure (essentially, industries designed to remove raw materials from Africa) and not manufacturing industries. Consequently, Africans were never taught any engineering or scientific knowledge, at least not the kind of knowledge that would enable them to manufacture their own raw materials or to maintain the infrastructure that Europeans left behind. At best they could sell raw materials to western countries, but western countries always have an advantage in international markets, because western countries control the means of production, and African countries lack the technical skills to develop mining technologies; thus, they have to outsource the work to western countries.
There have been times over the last century where African countries were on the verge of industrializing, but external events always prevented that. For instance, in the sixties many African countries were building up their textile industries. Western charities realized they could make money by bundling donated clothes and selling them to African merchants. Those merchants would then go back to their countries and sell the clothes. Because most of these clothes were from the United States, they had a cultural capital that clothes made in domestic industries lacked. Unable to compete with cheap clothes from the United States, textile industries went out of business, reversing the economic progress of those African countries. Generally, a country starts out in textiles or agriculture to industrialize. For instance, in the late nineteenth century Japan ushered all its resources behind selling cheap silk, and from the silk industry Japan was able to raise the money to build up its heavier industries. England built up its wealth in the nineteenth century from its textile industry, whose cotton was grown and harvested by slaves in the American South.(That is until the American Civil War. After the Civil War, Europe turned its eyes towards Africa). On a side note, the American Civil War was the first time that machine guns were used in war. Europe then used machine guns in the seventies and the eighties to carve up Africa.
The other alternative for a country to industrialize is to sell agricultural goods on the international markets. African nations cannot do that, because the United States flood international markets with its subsidized goods. African farmers simply cannot compete with farmers that are getting billions of dollars in tax payer subsidies.
Population growth, as mentioned, is another problem. Africa is not nearly as dense as European countries or Asian countries, but it is not developing at a rate fast enough to keep up with population growth. This is a problem in South America, and in the twentieth century it was a problem for China and India. Europe had colonies, which allowed them to shift domestic land towards manufacturing, thus enabling them to create the wealth needed to support growing populations. In the United States, diseases wiped out Native American populations, leaving behind a sparsely populated continent. The sheer amount of resources per capita in the United States greatly aided them in industrialization. Without colonies, China had to shift more and more of their land towards growing food, leaving less land for industry. Ostensibly, Africa could be like the United States, but African geography and topography is different from the United States and may not be as conducive to development. Additionally, as has already been mentioned several times in the thread, most of Africa lacks linguistic unity. Most of the developing Asian countries, including China, have the advantage of relative linguistic unity which enables centralized efforts towards development.
In China, for instance, wealth creation is generated by taxes and government efforts, not specifically by private enterprise. Private enterprises pay taxes to build factories and own land in China, and then the Chinese government uses those taxes to invest in infrastructure, education, and energy. Private enterprise does provide jobs for the poor, but those jobs pay way too little to help China to industrialize. To put it in another way, the factory workers in China lack the buying power to really make a difference in the greater economy. What these factory workers do is create wealth for private industries, who then pay taxes to the Chinese government. The Chinese government then uses those taxes to invest in infrastructure (better roads, water facilities, electricity, etc) that benefits those factory workers.
African countries, however, do not have the centralized clout to force taxes out of western countries. In fact, it is usually the opposite. African countries receive "foreign aid" which they then use to attract the services of western industries. Investors flood the country, speculators create a bubble, the bubble bursts, and the country is left worse off then before the foreign aid. Even worse, the country is still forced to pay back its loans, so all its tax receipts must go to paying foreign loans. This is a massive wealth drain, and it further prevents those countries from funding education or vital infrastructure.
You would be hard pressed to find any modern economy that industrialized through free markets. Great Britain passed many laws, including the Enclosure Acts, that favored landowners at the expense of workers and peasants. England used tariffs to destroy the textile industries in India, and then used their military to colonize India. France did not industrialize until its government started heavily investing in railroad and coal industries in the 1840's. Japan industrialized through national efforts and reforms, and most countries industrializing today, including China, have strong central governments. Mercantilism, not capitalism, is the first step in industrialization. Yet western countries often impose “free markets” on smaller developing countries, who simply cannot compete on the international markets. Those countries are simply drained of resources and raw materials. Repeatedly, when African countries have been on the verge of industrialization their nascent industries have been destroyed by international markets.
Weapons also play an important role in Africa. Those who rule are those with access to tanks and guns. As Ali Mazuri notes, “The slave trade coincided with the gun trade. African slaves arriving in the Americas helped the West to be more productive; Western guns arriving in Arica helped Africans to be more destructive...Political power in Africa often resides among those who control the means of destruction rather than among those who own the means of production.” Thus, the emphasis for most regimes is in acquiring weapons, not in investing in production.