The major reason for this is that European countries did not think Africa had much to offer.  This was true in the years before industrialization really took off and it was true in the years before all of the rest of the world had been divided up.

Africa did not seem very useful to Europeans because it was (for the most part) not suited for their colonies.  It was covered with desert or with jungle and was not suitable for farming.  It had diseases that prevented Europeans from living there and from raising animals there (like the "sleeping sickness" spread by tsetse flies).  Many parts of it had climates that were not acceptable to Europeans.  For these reasons, there was little to make Africa seem like an area that was worth colonizing.

This changed in the late 1800s.  As Europe became more industrialized, the mineral wealth of Africa became more important.  As Europeans colonized all of Asia, any European country that wanted more of an empire had to turn to Africa.  But before that, there was little in Africa to attract Europeans and so they did not colonize the continent.