How did the Industrial Revolution of the 19th century lead to the scramble for Africa?

The Industrial Revolution contributed to the "Scramble for Africa," as well as imperialism more broadly, in several different ways. 

First, the Industrial Revolution created an almost insatiable demand for raw materials, including metals, timber, rubber, and many others. Africa is rich in these materials, and European nations, and the industrialists who helped influence foreign policy, clamored for them. In the Congo, for instance, King Leopold of Belgium created his own company to profit from the harvest of rubber and other raw materials. His company treated the natives with shocking brutality that came to represent the worst of European colonialism. 

Second, the Industrial Revolution created a demand for new, secure markets for manufactured goods. Colonization created captive markets in places like Africa, and this helped to fuel the competition for colonies. Many Europeans feared that a lack of new markets would result in overproduction, which in turn would lead to economic depression. This gave urgency to the colonization project. 

Finally, the Industrial Revolution exacerbated the technological gap between the peoples of Africa and Asia and people in Europe. This was probably the single most important factor in facilitating the "Scramble for Africa." Europeans, armed with machine guns and other advanced weapons, were able to conquer African peoples.