Tribalism, in the oft-used sense of tribal prejudice or exclusiveness is simply racism that is not based on the grossest differences of skin colour, but on more subtle ethnic distinctions.
To give a traditional example, Hutus and Tutsis are not all that different, but they have come into conflict based on their ethnic differences in Rwanda and Burundi.
Many Xhosas and Zulus likewise have tribalistic prejudices against each other in South Africa.
Tribalism is still an impediment to African unity. As the example of Rwanda shows, the perception of ethnic otherness within Africa still holds Africa back.
It is easy for Westerners to assume that the inhabitants of Africa are huge, amorphous tribe of well, black people. This view is completely false. It is akin to thinking that both a Catholic Irishman and a German Lutheran view each other as kinsmen and themselves both primarily as white people.
To take this over into Europe, tribalism is the reason why Protestants and Catholics kill each other in Ireland, why various groups in The Balkans are at each other's throats.
As an aside, White South Africans are sometimes referred to as the "White Tribe" of Africa. This is also completely false. There are two white tribes: the English speaking white South Africans and the Afrikaans speaking white South Africans, the Afrikaners.