Okay so the border issues suffered by many African countries are not at all uniform across the whole continent. Africa is a huge continent much larger than Europe and encompasses a lot a countries many of which in themselves are quite large.

The first issue is that when colonialism started there was little to no regard for creating colonies that encompassed ethnic groups or political polities. Those countries involved in colonialism were largely interested in the economic returns on the colonial investment with the lives of the people living there being a side thought at best.

An example of this can be found in the now notorious Belgian Congo. The Leopold II is vilified nowadays for his appalling policy towards the Congo Free State. The Congo Free State was carved out of central Africa following the 1884 Berlin conference and took little regard for the polities in existence beforehand. Since its quite hard to explain this without maps here are a couple that might help. Here is a modern day map of the Zambia Congo Border. Here is a map of the very rough pre-colonial borders of polities in the area.

So the important states to look at are the two Lunda states (The Mwata Yamvo's kingdom and the Kazembe's Kingdom) and the Luba and Lozi. These states which were essentially part of their own network and could probably have individually formed countries prior to colonialism have been split down the middle with the Zambia/Congo border. One side would be the Congo Free State, the other Rhodesia. Now there are other factors at work here too, the violent introduction of long distance trade, interference from Arab Swahili traders causing widespread violence and panic in the late 19th century all contributed to the decline of these states too. But obviously the borders here are not particularly natural.

So if we fast forward to the Congo Crisis of 1960 we see that the Katanga area that attempted to secede was constituted of the area in the maps. A lot of the justification was that these areas are ethnically and nationalistically different to the northern areas of the Congo. Whether or not there was true nationalistic feeling from the citizens of Katanga is another question in itself, but the borders drawn up upon the end of colonialism are certainly problematic. I don't think it would be fair to say that there would be no conflict without the borders, there was certainly conflict between the Lozi, Luba and Lunda before them. But the somewhat arbitrary borders it certainly contributed to the conflict that was brewing in the Congo.

I hope that this helps give a concrete example to how colonialist Borders were drawn in Africa and how it is relevant to understand more recent conflict. Once again this is not a uniform situation, some each state has its own unique post colonial heritage. Another that is somewhat similar to the Congo is it's southern Neighbor Angola. However, other states such as its Rwanda which I mentioned below had fewer problems to do with borders but similarly encountered much violence.

You might be interested to read about the concept of a rentier state: http://en.wikipedia.org/wiki/Rentier_state

This is basically a government that gets most of its revenue from natural resources. So in states in Africa, in addition to having diverse ethnicities that may not identify as "Chadian" or "Congolese" the state itself has no vested interest in the people.

If you think in terms of government being a service, and people being consumers, a country like France has a vested interest in the productivity and participation of its people. A richer economy means a richer government.

In a rentier state, the customer is not the people but whoever is buying the natural resources, usually an international marketplace. The government is essentially a organized business outfit whose goal is to maintain a monopoly of violence (police, army) to control the natural resources to fund itself. It doesn't care about being "Chadian" or "Congolese" either, or at least it doesn't have much incentive to do so.

This is why you see a lot of strong men dictators in Africa. You can see how these two factors--people who don't identify with country and country that doesn't need people--can work together to prevent a national identity from forming.

The greatest example of this would be the Rwanda Genocide of the ethnic minority Tutsies by the dominant Hutus. When the Belgians were in power, they lifted the Tutsies above the Hutus based on the fact that they appeared more "Western" than the Hutus. The absolutely insane part of this was the immensity and scale. In around 100 days, upwards of 1,000,000 people were killed, and these people were predominantly hacked to death with machetes. It was an extremely bloody, and violent consequence of colonialism, and the drawing of borders. We'll never know if they had split the two groups into to different countries whether or not it would have happened via war, but it is still the best example that comes to mind.

Source: Several College Level Anthropology classes have delved into the matter.

edit: Grammar