European colonial borders contributed to post-colonial conflict because they were basically arbitrarily drawn—or drawn in a way that prioritized the interests of Europeans—without considering the diversity of the continent.
In 1885, colonial borders were drawn by mutual European consent at the Berlin Conference, an agreement that basically ratified European claims to territory gained through conquest. Because colonial borders often became the basis for post-colonial nation-states, peoples with ancient rivalries and grievances—and, at the very least, little common heritage—were crammed together into modern nation-states. What made this particularly toxic was that Europeans often (in the interests of maintaining their empires) favored one ethnic group over another. When European power was removed, clashes often developed over who would control the new state, sometimes with violent consequences.
In Rwanda, for example, the two largest ethnic groups were the Hutus and the Tutsis. Under Belgian colonial rule, the Tutsis were given preferential treatment; the were granted education, prime farmlands, and positions within the colonial bureaucracy. This was a deliberate policy rooted in the Belgian understanding of race and racial hierarchies as well the need to avert unity against their colonial regime. Consequently, it created a legacy of resentment between the two peoples that exploded into conflict repeatedly after independence in the 1960s. It was the background for the unspeakable genocide of over 800,000 Tutsi people in 1994.
Similarly, modern Nigeria was created out of two regions that were merged together by the British in the early twentieth century. This brought the majority-Muslim North into conflict with the predominately-Christian South, and contributed to a series of violent conflicts. Because the British's motives were strategic—they hoped to connect the northern part of their holdings in the region to the Atlantic coast—they did not take the political and social realities on the ground into account.
In this way, the arbitrary establishment of borders by European powers contributed to decades of conflict in Africa.