Also why were Britain, France, Germany, and Italy interested in Africa in the first place? What strategic or economic purposes did their African colonies serve?
The Conference was held just as the scramble for Africa gained momentum, setting the rules for colonization of the continent.
One of the first points made during the Conference was the prohibition of slavery in Africa. This was mainly done to gather support from the European public and bolster the idea that Europe was bringing civilization to a savage and barbaric land.
The Congo Basin was a hot topic during the conference. It was confirmed to be the private property of King Leopold II of Belgium, but arrangements were made to ensure free trade and openness to all European powers.
Concerning expansionism and territorial claims, the signatory powers agreed on the Principle of Effective Occupation. This meant that a single nation couldn't lay claim to a portion of land on a whim. For that land to belong to a European nation, they needed to make treaties with local leaders, establish an effective administration and install a martial presence in the region. In other news, you couldn't just call dibs on the Horn of Africa. You needed some physical evidence that your nation is the undisputed master of that land.
The Principle of Effective Occupation was instituted in order to minimize conflict over land. In 1700's America, France and Great Britain constantly butt heads over territory because there was no concrete system in place.
Now, onto the matter of why the Scramble for Africa happened. You'll see that the question we want to really is ask is how it happened.
During the 1800's, exploration into Africa by wealthy Europeans became more and more commonplace. What began as curious adventurers exploring an alien land evolved into a more practical purpose. Potential markets, trade routes, and exploitable resources became cataloged and recorded. This peaked the interest of European capitalist. As the colonies of America became independent nations, Europe needed alternative sources of raw materials. They needed rubber, coffee, sugars, and metals to feed the first factories. All of this was within Africa's dark interior.
You may ask why the nations of Europe didn't colonize Africa, a continent right under their noses, before the 1800's. Well, they did to an extent. Small colonies were established by the Europeans, dotting the African coast, fortified against natives while brimming with merchants who traded with them. But why did they wait to long to expand inwards and develop real colonies? Because of environmental determinism, the fact that technology makes inhospitable lands viable for habitations. The rivers of Africa could now be navigated via steamships. Diseases like malaria and yellow fever could be fought with new medicines. European breech loaders eclipsed African muzzle loaders in effectiveness.