This question could potentially lead to some very interesting responses, but it is overly broad.

Colonization of Africa can be defined by several time periods and happened differently throughout the continent.

Greeks were colonizing Northern Africa in 6th Century BC. Phoenicians had established colonies as early as 12th Century BC, Carthage (modern day Tunisia) being the most successful result. Carthage shifted hands after the Third Punic War to Rome, and subsequently was ruled by the Vandals, then Rome briefly again. In 698 AD Muslims assumed control after the Battle of Carthage. The period after the spread of Islamic influence in Africa was dominated by slave trade, and is probably what left the continent most susceptible to outside influence.

The Scramble for Africa, and the Berlin Conference are what shaped late 19th and early 20th Century AD European Colonialism. This would lead to European nations intervening in many local disputes and wars, afterward stepping in and installing their own ruling bodies.

This is of course a very abridged history. Kevin Shillington's "History of Africa" is a great resource for the subject.

The short answer to your question though is slavery.

Could you define a period? European empires have gone back and forth to Africa several times throughout history.

It's a lot to talk about. The Scramble is an interesting subject that covers a lot of late 19th century international politics.

First of all, let's establish one thing: Africa didn't resist European colonisation because it couldn't. It had no unity, no coherent political structures that could have managed to work together. The slave trade was the only link between people from Bulawayo and Gao. It was with the help of several of these slave traders that the first european explorers managed to survive. Livingstone, for example, relied on slave caravans for gunpowder, pots, cloth, beads, medicines, porters, even letters from back home. Btw, did you see that I mentioned the word "porters"? Africa was hard to explore (and even harder to conquer) because of the tsetse fly. The sleeping sickness, the parasitic disease transmitted by these insects, were the bane of any animal that could be used in an expedition. That's why you used only human labour, strong africans that would carry your luggage around. Not that practical.

Second of all, colonisation wasn't an exclusive European thing. We know about Ethiopia resisting against Italian aggression in 1896 at Adwa but what common knowledge seems to ignore is that by that time Ethiopia had become an Empire as well, conquering and colonising near-by territories, using weapons purchased from European traders. Even earlier, the khedive of Egypt had extended the territory of his realm towards Lake Victoria, carving an enormous area of influence in Sudan. In this attempt, he made use of European governors and military commanders: Charles Gordon of Khartoum fame, Samuel Baker (discoverer of Lake Albert) and Emin Pasha, the german governor that was to become a search target for subsequent belgian, english, french and german expeditions.

Third. Out of the African polities that could have resisted, only Ethiopia managed to, helped, as I said, by its transformation into a colonising power. The rest were weak, semi-wild "states", dependent on Europeans for firearms and ammunition. Another thing to know is that the conquest wasn't a simple affair. Sometimes you went to the chief of a tribe and made him sign some kind of treaty with the leader of your country; sometimes you'd pay for him to take arms against a rival. Everything was complicated by the fact that this process was strictly controlled from the European capitals. King Leopold of Belgium, the guy that pretty much started the whole Scramble, had to first pay Stanley to explore the Congo river for him. Then created an association with the goal of ending slavery and bringing civilization, commerce, even Christianity to the poor african people. Then promised the English that he would deliver the Congo area to them if he wouldn't manage to control it; then made the same promise to the French. Then created the colony of Congo as a free-trade state. Then made it into a hell.

Public opinion was another essential factor of the period. For most of the 19th century, the British public had been unenthusiastic about colonies - so Great Britain made no great strides until the imperialist enthusiasm of the 1890s. The French started the madness after the humiliation of 1870. Bismark desired no colonies but the german public wanted them - so in 1884, Bismark completely changed his mind and turned the Scramble into a race.

Source: The Scramble for Africa by Thomas Pakenham