An interesting analysis on this question was brought up by Jared Diamond author of "Guns, Germs and Steel" and I believe it is a more accurate answer to the question than that offered by Lennart Regebro (no offense intended to that author!). While Regebro is certainly true in explaining major factors to the continuation of many African nations relative poverty, it ignores the root cause of the initial wealth in-balance between Europe and the U.S. in contrast to many African nations. According to Mr. Diamond's analysis, while Africa in general is rich with many types of natural resources, it was initially poor in the resources most important to early civilization, domesticable plant and animal life.
First, Mr. Diamond identifies 14 major domesticable animal types of which five are most important those being sheep, goats, cows, pigs and horses. The lesser animal types include the Arabian camel, Bactrian camel, Llama and Alpaca, Donkey, Reindeer, Water Buffalo, Yak, Bali cattle, Mitha. It is important to point out that NONE of these animals have ancestors in sub-Saharan Africa; 13 of the 14 DO have ancestors in Eurasia. Most animals in Africa, particularly in the Sahara, are either difficult to domesticate or do not provide sufficient quantities of meat, milk, or labor. Furthermore, four of the five major domesticable plant types: wheat, corn, rice, barley, and sorghum are found in Eurasia. Climate was also a factor as it promoted the diffusion of both domesticable animals and plants throughout Eurasia while hindering their spread through Africa and the Americas.
All this slowed the development of civilization in Africa and subsequent technological advances, while assisting development in Europe and Asia. Hence, while major empires such as the Sassanian, Han Chinese, Greek, Roman, Mesopotamian, Babylonian, Mongolian etc all derive from Eurasia, Africa has had less success in cultivating sedentary agricultural societies necessary to develop empires and subsequent technological/societal advancement (likewise the environmental devastation caused by many early farming techniques helps in part to explain the decline of the empires of the once-fertile crescent and the now relative poverty of non-oil bearing Arabian states).
Colonialization is a major factor indeed, and while not a symptom of poverty it has greatly exacerbated it. The development of colonies has created a continuing drain on African nation's resources and the destructive political/military intervention of outside powers (note current destabilizing American wars in Yemen and Somalia). However I would note for the asker that the difference between the colonization of America and that of African nations is more profound then the author realizes. In the former Britian sought to develop widespread settlement in North America, whereas in the latter European powers have instead sought widespread control of resources. Thus many of the British settlers in North America grew powerful as a result of owning/working the land and the largely beneficial policies/support of Britian (despite taxation w/out representation, the colonists did receive a great deal of military, technological and financial investment), whereas African nations were subject to massive resource theft and control from a small minority of European colonists. The key point here is that American colonists benefited from the advantages bestowed by their client empire (which in turn was granted them by luck), whereas American natives and Africans have suffered precisely because of said advantages to early Eurasian development.