Indirect rule was a colonial administrative system employed by the British using African natives to administer their own affairs; conquered kings, chiefs, elders among others, were used to administer their subject on behalf of colonial masters.
among others, were used to administer their subject on behalf of colonial masters.  

Reasons for the Use of Indirect Rule
1.  Lack of enough British personnel to execute colonial duties e.g. by May 1900 the British government had approved only 42 officials thus the need to use Africans.
2.  The existence of centralized institutions like the Emirs in Sokoto caliphate in northern Nigeria and Kabaka plus chiefs in Buganda these had substantial influence among the their subjects
3.  Indirect rule was financially cheap, traditional leaders were less expensive than the whites officials; they only needed petty gifts like old clothe, chairs, old coats.
4.  The British thought the policy would lesson/control on African resistance. This is because Africans would not want to harm their local leaders like they would do to whites.
5.  It is claimed that the British wanted to preserve and maintain African traditional institutions.
6.  It is also believed that the British unlike the French looked at colonies as separate entities that required minimum interference.
7.  The British intention was purely to exploit colonies rather than invest in them through paying expensive administrators.
8.  It is also argued that the British wanted to train Africans and equip them with skills of leadership for eventual serf rule.
9.   Indirect rule was seen a solution to the problem of language barrier.
10. African leaders were used to environment in their countries than their European counterparts and thus could be more effective.
11. The poor transport facilities in African states necessitated the use of local chiefs that would ably move deep village while the European officials were stationed at more accessible centres.