That's like asking what makes babies cry. There are too many different causes to explain it fully, but the origin of many of these problems came from "the scramble for africa," when at the Berlin Conference of 1885, European nations including Britain, France, Portugal, Germany, Denmark, Spain, and Belgium met in order to divide up the African continent amongst themselves. In the process, they paid no attention to the territories of various ethnic groups. Some groups found themselves neighbors of others they had long warred with - some groups found themselves split down the middle. This all relates back to interstate conflict via the issue of sovereignty. Ethnic groups war with each other over land as well as the resources reaped from these lands. On a continent where drought and famine run rampant, land is the most important resource.
This explanation really referrs to small-scale conflict, but large-scale conflict, meaning that which involves heads of state and/or military involvement, also is based on sovereignty. Think about it. Most of these countries are only 40-50 years into their independence, which they had to fight global superpowers to achieve. Even the African UNION's charter is devoted mostly to respecting one another's borders and rights to rule their own lands - SOVEREIGNTY. It's about resources, it's about machismo, it's about ethnic conflit and high-level corruption... interstate conflict in Africa is a huge topic. If you narrow your question down a little, I'd be happy to help. Email me (I have a Master's Degree in African Politics, so you can trust me!)