Prince Henry the navigator's motives for promoting the exploration of the African coast were:
Resources from Africa: Slaves, sugar, and gold.
Spread of Christianism: the exploration of new territories gave the possibility to evangelize.
Renaissance spirit: Henry´s desire for fame and glory is part of the spirit of men of the time.
Spirit of adventure and navigation tradition: Portugal faced the Atlantic Ocean, therefore they had a large sailing tradition on open waters.
Political stability within Portugal permitted exploration abroad.
Technological advances for navigation: developments like the Carabel, the Nao, the compass, the portulans, and the astrolabe permitted navigation on open water and unknown territories.
You can learn more about Henry the Navigant in the link below: