There are a lot of complex issues bundled up in this question that might need several specialists. It might help if you could pin down exactly which parts you are interested in. Off the top of my head: oceanography, construction techniques, financial development (eg East India Company - stocks/companies, Bank of England - credit managed as a tool of government, etc), markets, improvements in food preservation, mathematics, replenishment depots on routes, politics, access to overland routes, Muslim trade networks in the Indian Ocean, and so on and so forth, all play a role.

Is it the evolution of large ships? That is not a linear thing. The original age of exploration was opened up by very small craft such as the lateen-rigged caravel, which was fast, maneouverable and could sail into the wind, opening up routes that were previously difficult. Late Age of Discovery exploration vessels such as Cook's Endeavour were also small. Until late on in the industrial revolution when iron and steel construction made large, relatively cheap, strong long-lasting sailing vessels possible, merchantmen were generally pragmatically medium sized, or medium-large for some Indiamen. There were exceptions, for example the Peter von Danzig , a Hanseatic carrack built in 1462, was 800 tons and 51m long, larger than most contemporary naval craft. But she operated in the Baltic and North Sea and played no part in the Age of Discovery. It usually took a Navy to make the high costs and endless maintenance of very large wooden vessels on long voyages worthwhile, and there were large naval vessels prior to the Age of Discovery, the 10th century viking longship Ormen Lange is put at around 45m, as were Roman quinqueremes. I am not touching the arguments about how large 15th century Chinese treasure ships were, not for love or money.

What drove the Age of Discovery was the changes in the land routes in Asia for the Silk Road. The Monguls took over Persia and cut off two routes (land from China and sea from India to Persia) to getting goods to Europe. The Europeans became very interested in having ships that could carry large amount of goods and less men for sea routes that went around Africa to China and the East Indies. Portugal and the Dutch lead and worked down the coast and eventually made it to India.

A good introduction to the above issues and how different European powers acted can be found in Murray RothBard's Conceived in Liberty, Vol 1, Part 1. Europe at the Dawn of the Modern Era. This book is freely available online.