Why did the Portuguese travel to Africa?

The Portuguese travelled to Africa because they owned it. It's not a joke, we did that because we, alongside the Spaniards, were the most advanced country in the world at the time, so much so that the world was divided between Portugal and Spain in equal halves (check the Treaty of Tordesillas).

In 1481, the papal bull Æterni regis had granted all land south of the Canary Islands to Portugal. On 4 May 1493 the Spanish-born Pope Alexander VI decreed in the bull Inter caetera that all lands west and south of a pole-to-pole line 100 leagues west and south of any of the islands of the Azores or the Cape Verde Islands should belong to Spain, although territory under Christian rule as of Christmas 1492 would remain untouched. The bull did not mention Portugal or its lands, so Portugal could not claim newly discovered lands even if they were east of the line. Another bull, Dudum siquidem, entitled Extension of the Apostolic Grant and Donation of the Indies and dated 25 September 1493, gave all mainlands and islands, "at one time or even yet belonged to India" to Spain, even if east of the line. The Portuguese King John II was not pleased with that arrangement, feeling that it gave him far too little land and prevented him from possessing India, his near term goal (as of 1493, Portuguese explorers had only reached the east coast of Africa). He opened negotiations with King Ferdinand and Queen Isabella of Spain to move the line to the west and allow him to claim newly discovered lands east of the line. The treaty effectively countered the bulls of Alexander VI and was sanctioned by Pope Julius II via the bull Ea quae of 24 January 1506.

These voyages were made in the name of Geography and commerce, and since Africa and Brazil were on 'our side' of the world, we travelled there to see what was in fact ours.