In addition to the reasons already stated, it is important to realize that there was European competition for colonization of Africa, from Germany, Portugal, France, and Belgium, among others, which had or were in the process of colonizing substantial portions of Africa. Colonization was a competitive process, and every area the British could colonize was an area another country could not. I always think of this as like the game Risk, where one's position is considerably strengthened the more one has of a continent, although colonization was by no means a game, of course, and had dreadful moral implications, which haunt us to this day. For Great Britain to "grab" another piece of Africa strengthened it vis-a-vis other world powers, though.
Furthermore, the British, an island nation, had nowhere to go to expand economically or politically without colonizing. The small island nation saw itself as having no other way to "grow." The countries of Europe, for the most part, were well-defended, fairly well-established political entities, which would have been costly to conquer, so African expansion was a logical choice, being peopled by those who had few, if any, defenses against colonization.