Why did Europeans explore?

Answer 1

Trade and treasure was always at the bottom of it. Although curiosity about unknown places and a sense of 'can this be done?' (think Columbus' and Magellan's travels) certainly played a role, the idea always was to discover places where spices could be bought or gold could be found.

Medieval Europeans were very much aware that their dependence on the existing overland supply routes and on Venetian and Arab merchants led to supply always being less than demand, and - as a result - to skyrocketing prices. Basically, the 'exploring' nations - Portuguese, Spaniards, Dutch and English - were trying to corner the markets for themselves.