Why did European countries engage in imperialism?

European countries engaged in imperialism for a number of reasons. For one, they sought new secure, captive markets for manufactured goods. This would be profitable and guard against the danger of industrial overproduction, which many blamed for economic downturns in the late nineteenth century. Along with this, many industrialists and investors also wanted access to the cheap natural resources and labor to be found around the world. So colonies were seen as business opportunities.

Europeans...

European countries engaged in imperialism for a number of reasons. For one, they sought new secure, captive markets for manufactured goods. This would be profitable and guard against the danger of industrial overproduction, which many blamed for economic downturns in the late nineteenth century. Along with this, many industrialists and investors also wanted access to the cheap natural resources and labor to be found around the world. So colonies were seen as business opportunities.

Europeans also had ideological motives for expansion. Many Social Darwinists thought that white Europeans were superior to non-white peoples around the world, and that they should have no qualms about conquering them. Indeed, many believed that it was the obligation of Europeans to bring culture, technology, and Christianity to others deemed primitive and "savage." 

Social Darwinists also tended to view relations between nations as a brutal, pitiless struggle, and the process of imperialism was thus also a "race" to gain the most territory. Great Britain was far in advance of the others, having control of a massive empire by the 1870s. France and the new nations of Germany and Italy were eager to gain territories to rival the British and each other. There was a sense in which the old territorial competitions between European nations on the continent gave way to struggles in colonial lands around the world. These conflicts were somewhat managed by the Berlin Conference of 1885, which effectively carved up the continent of Africa between the European powers. 

These motives, economic, ideological, and strategic, were the primary motivators for European imperialism.