Fausto Bordalo Dias "O barco vai de saída"
Fausto Bordalo Dias "O barco vai de saída" (The boat is setting out)
Here are several possible answers I've come across reading about Portugal. I'm not sure about how much importance to give each one.
1. Portugal is located in the far southwest of Europe, squeezed between the mountains and the sea. There's not really anywhere else to go in Europe. Across the mountains are “Castilians with knives”.
2. Fishing has always been a key industry, so Portugal had the sailors. Also you have to go a long way for some catches (e.g. to Newfoundland for cod), so the sailors had deep-water Atlantic sailing skills, not more coastal Mediterranean experience.
3. The best land in Portugal is along the coastal strip in the north and centre of the country. As you go south (into the Alentejo) it gets dry - not an overwhelming problem for modern agriculture but a big challenge in the past. Till you get to the far south coast (the Algarve), which has some potentially fertile mountains and rivers. But, back in the past, to make much use of the Algarve you really needed to control both sides of the sea - the European and African coasts. Otherwise raiders would steal your workforce or set up their own castles and mini kingdoms. So immediately after driving out the Muslim Moors the Portuguese Christian kings set about seizing land on the African side too. (Which of course the Moors had had themselves - it was the only way to make the Algarve viable).
4. With the Algarve conquest the new Portuguese landowners had a labour shortage. The peasants further north were needed where they were, so as they explored south the Portuguese were also looking for slaves.
5. While sailing the seas the Portuguese came across several previously undiscovered, often uninhabited but useful or resource rich island groups. These include the Azores, Madeira, the Canaries (now Spanish but discovered by the Portuguese) and the Cape Verde Islands (now the independent state of Cabo Verde). Madeira for example was a rich source of wood, useful in a sailing age. Also on one of these voyages they discovered Brazil, officially discovered in 1500 though the Portuguese might have been keeping this information quiet for negotiating advantage.
6. When the Ottoman Turks captured Constantinople in 1453, this disrupted the trade routes from India and China to Europe. Previously established European intermediaries from Venice, Genoa etc had bought from other Muslim and Christian merchants and shipped the goods west to other parts of Europe. Now this was difficult, so the idea of finding new routes to India and beyond really took off. The Portuguese were well placed to explore the route south to India.
7. The Knights Templar (yes them!) were among the intermediaries who had previously traded between Christian Europe and the Muslim Levant. When the papacy reluctantly abolished them (under pressure from the French king who was seizing all their assets in France) many fled west. At that precise moment the Portuguese monarchy established a new religious order called the Order of Christ. This seemed to be instantly blessed with great trading, mapmaking and sailing skills. Whatever you think about the Templars, the Order of Christ was indisputablely heavily involved in Portuguese voyages of discovery from then on.
8. Once Portuguese explorers had discovered the route round Africa to India, Portugal immediately outfitted a large war fleet to go to India and establish trading relations. Vasco da Gama wasn't some small time explorer or navigation enthusiast pottering around looking for new knowledge for its own sake. He was an appointed royal commander of a heavily armed trade mission. Money became Portugal's prime motive, along with continuing the fight against a Muslim power that had a stranglehold on trade in the eastern Mediterranean.
9. Last but not least: it gave the Portuguese more stuff to sing about.
I have posted a version of this answer on Quora, a popular question-and-answer website.
See Ian Stobie's answers about Portuguese history (and music) on Quora
For music the answers on portuguesemusic.info are usually more complete ("canonical") than on Quora, with longer extracts and translations. That's because this is not a commercial site like Quora, allowing greater freedom under "fair dealing" copyright provisions. However, on Quora the sometimes bizzare questions prompt you to range far and wide.