The FAQ covers this question. the TL/DR answer is African civilizations have been pretty much on par in terms of developmental levels with the rest of the world through much of human history. European colonialism created and propagated a notion of a backwards Africa that existed out of time that ignored the civilizations that lived there. This active disinterest in the continent's history, coupled with the steady erosion of archeological evidence, creates the impression that Africa had never possessed any advanced polities or empires. The historical reality was the exact opposite.

It's a bit more that Africa didn't fall behind, but Europe leaped ahead of all others to the point that no civilization was left untouched by its advancements and 2 other continents (the Americas) had most of their native identify erased. Africa is lucky that powers like Mali existed to stir Europeans to trade with them rather than to try full on military conquests like occurred in the Americas. Of course, the dramatic changes in Europe from the 1600s to the 1800s brought Europeans the power to counter any local king or tribe with ease during Africa's main period of colonization.

As for what lead Europe to leap frog, there must be hundreds of threads dedicated to that.

As /u/kieslowskifan mentions, Africa has had many civilizations as advanced as you'd find elsewhere.

That said, I'm not sure that time is the most important variable, or that we should even expect it to be. Real life isn't like Sid Meier's Civilization: progress isn't linear, and it certainly isn't independently researched everywhere. You don't spend 300 bars of science in order to invent writing, you build up cities and make a more complicated civilization until someone says "Keeping track of things is hard. Why don't I mark up some clay or knot these strings to help me remember?" and someone else says "why don't I also decide on a way to note what kind of thing I'm counting?" or you meet someone who says "let me tell you about this wonderful writing stuff I've just learned about!"

Many of the most important discoveries have only been made a handful of times and spread out throughout the rest of the world.

Agriculture and writing, for example, were independently invented several times. The first location for both was Mesopotamia, and sometimes thousands of years passed between independent reinvention. Since the first location to exit the paleolithic was Mesopotamia, should we expect Iraq to be one of the most developed countries? For another example, the wheel was independently invented at most a handful of times: it appeared in Central Europe, the Caucasian mountains and Mesopotamia essentially contemporaneously, and then was never again independently reinvented.

I should point out that technically the 'been there the longest' element is irrelevant. We only know of one wave of 'civilisation' and that occurred after the last Ice Age, at which time Humans had reached most parts of the globe, thus it was an 'even playing field' in that respect. Secondly that all current humans societies have been developed since Homo Sapiens came to be, some are just are not in their original starting spot and some are thus their is no real African 'head start'.