Why? Well, the biggest reason that Europeans were able to extend their grasp over so much of the world was the same reason they wanted to do so in the first place, industrialization. Nationalism played its part, of course. European states saw it as a real bonus to be able to say that they had colonies, so much so that a children's rhyme in an ABC for Baby Patriots went, C is for colonies, rightly we boast, that of all the great countries, Great Britain has the most. But it was mostly, not to get all Marxist on you or anything, about controlling the means of production. Europeans wanted colonies to secure sources of raw materials, especially cotton, copper, iron, and rubber, that were used to fuel their growing industrial economies. And in addition to providing the motive for imperialism, European industrialization also provided the means.