Henry The Navigator lived in a time when there were no water conduits or canals (like the Panama Canal) for ships to move through for a more efficient route. At that time in the 1400's, the only known way to travel from Europe to Asia was by land with the Silk Road, or around Africa with a ship. When I say "around Africa", I mean around its southern tip.
In the early 1400's, (specifically 1415), Henry, along with his father and brother, explored Africa and hoped to use the continent's resources to benefit Portugal. As the rush to Asia began, Prince Henry helped Portugal be the first to find a viable water route. He designed a new ship called the caravel, which gave Portugal the capability to sail faster to greater distances. This helped Portugal sail to the "Green Sea of Darkness" (aka, the Equator), a feared section of ocean by legend. It took twelve years and fourteen voyages to reach the Equator, in which Henry sent more ships to explore the coast of Africa in 1444-1446. Henry's last sponsored voyage (he did NOT sail on the expeditions himself) managed to reach more than 1,500 miles down the coast of Africa. His sponsorship in the exploration of Africa's coast would ultimately set the stage for explorers after him.
After Henry's death in 1460, the voyages continued. In 1487, Bartholomeu Dias reached the Cape of Good Hope, in what is now modern day South Africa. However, he was forced to turn back as his voyage hit massive troubles along the way. Ten year after Dias reached South Africa, Vasco De Gama sailed all the way to India and set the first sea route to Asia.