Some of the key motives for British colonial settlements included:
1. Economic gains. Britain saw colonies as opportunities to acquire new markets for its goods, resources like timber and precious metals, and cheap raw materials for its industries. Colonial trade allowed Britain to grow its wealth and power.
2. Strategic benefits. Colonies could serve as military bases, coaling stations, and sites for naval dockyards. This expanded Britain's global influence and power projection capabilities.
3. Spread of Christianity and "civilization". Many British leaders viewed colonialism as a means to propagate Christianity and what they considered to be superior European culture and values.
4. National prestige. found and rule over far-flung colonial empires was considered a mark of a great nation and increased Britain's global prestige and influence.
5. Population overflow. Some colonies, especially in North America, served as places to send excess population from Britain, especially unemployed workers or prisoners.
So economic motives were a primary factor, along with strategic calculations and a desire to extend British national power and reputation on the world stage. The desire to spread Christianity and "civilize" indigenous peoples was also an important ideological motivation.