On a broader level, industrialization had caused much of the competition and push to colonize places in Africa, particularly Kenya, where the British had been administering land for years prior to 1895.

Once the Industrial Revolution changed the economies and daily lives of Europeans, particularly the British, there was a need for more raw materials to continue factory work, both coal and rubber for the factories themselves, and the natural resources that would later be turned into manufactured goods for sale across the empire. With the Atlantic Revolutions, Europeans had lost a lot of access to natural resources that they could previously rely on through their early modern mercantile economies. With a still rising demand for industrial goods, Europeans turned to Africa in the early nineteenth century. Europeans also competed for this land; at the Berlin Conference of 1884–1885, seven European nations carved Africa up into pieces based on their military and economic interests.

Some areas of Africa were taken and turned into imperial colonies, exploited for their land, laborers, and natural resources. Other areas, like Kenya, were settlement colonies. The British found that Kenyan land was fertile and could be used to grow a British settlement in Africa. Furthermore, access to luxury goods like ivory encouraged the British to grow their economy. Kenya was also centrally located (relatively) to Britain's other African colonies and economic interests. The British were also building a railroad through Kenya, and colonizing it meant they could have more control over it, while edging out competitors like the Germans to the South in Tanzania.

Once Kenya became a colony in 1895, the British started to settle it in the early twentieth century.

The British had been colonizing what is present-day Kenya for many years prior to the establishment of the East Africa Protectorate in 1895. The area was administered and economically exploited by the Imperial British East Africa Company (IBEAC), which was chartered by the British government in 1888. Effectively, this meant that the administration of British East Africa was privatized, contracted out to a private business.

For a few years, this arrangement seemed to work rather well, at least for the British. But in 1895, the IBEAC collapsed, bankrupted by a costly civil war, from which it nevertheless emerged as the victor. Even so, British East Africa remained a source of considerable wealth for the Empire, and so the British government stepped in and proclaimed the area a protectorate, an arrangement whereby one state is controlled and protected by another.

With British East Africa now under the protection of the British government, the chances of a civil war breaking out, of the kind that had brought down the IBEAC, were greatly diminished. Now that the region was directly administered from London by the Foreign Office, the British Army could be brought in to quell any domestic disturbances, thus protecting what remained a highly lucrative colonial endeavor.

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. 

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.