There are a number of reasons why the British colonized Kenya. In general, though, they are the same types of reasons that the British had for most of their colonization. The British colonized Kenya for economic considerations and for increased power.
The British saw Kenya as a potential source of wealth. It had raw materials like ivory. It also had areas that seemed to have the right sort of climate and soil for European settlement and farming. These sorts of economic factors made it attractive.
The British also saw colonizing Kenya as a way to get more power. They felt it would give them more prestige in their competition with other European powers. They also thought it might provide more security for their hold on the Nile (which was important because it dominated Egypt).
In these ways, the British colonized Kenya for reasons of economics and of power.
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.
The British had several reasons to colonize Kenya in 1895. These reasons were similar to the reasons why Great Britain colonized other places.
One reason was economic. By colonizing Kenya, the British would have a place where they could trade the products made by British industries. This would help the British industries. Kenya also could provide Great Britain with needed resources. Kenya had good areas of land for farming, and the British hoped to take advantage of this. However, there were issues that limited the benefit of the good farming regions. Diseases and overuse of the soil were two issues.
There were political considerations in the colonization of Kenya. Other countries were colonizing Africa. The Germans were also making a move to colonize Kenya. The British needed to act if Great Britain wanted Kenya to be a British colony. Since countries were competing for limited areas of land available for colonization, Great Britain needed to act if it wanted to enhance its status as a world power.
Kenya could serve a military purpose if war broke out. Since there was fighting in Africa in World War I, having Kenya has a military base proved to be advantageous for the British government in World War I.