They wanted access to the eastern trade routes which were (at that time) dominated by the Ottoman and Persian Empires.
It was believed that they could get access to the silks of China and the spices of India and the Indonesian Archipelago by finding alternative routes. The Portuguese sailed south, around Africa's Cape Bojador and the Cape of Good Hope, and established trading stations (often at gunpoint) at Goa and Melaka, while the Spanish sailed in the hope of reaching the Indies via a westward route.
England's navigators tried to reach the Spiceries (as they called the Spice Islands) by sailing north; they believed that they could find an open passage to the islands by sailing via a NorthWest Passage. This failed, as did the attempt to reach the islands by sailing North of Russia. Sometimes you have to wonder what they were thinking!
While access to the luxury goods of Asia was the overriding motivation for the first voyages, much of the colonisation and conquest which followed was the direct result of trying to check the ambitions of rivals; for example, Britain became involved in India in order to check French power in the region, and much of Spain's motivation to sail west was to try and head off the growth of Portuguese economic and maritime power in Asia.
Of course, once Spain found the rich civilisations of Mexico and Peru, the appropriation of their wealth became the overriding consideration, especially as the gold and silver could then be used to purchase the luxuries that Europe craved. Galleons laden with silver from the mines of Potosi sailed every year to Spain's colonies in the Philippines, and on to regional markets where the silver would be exchanged for silks, spices, and porcelain.
Colonial activity ensured that luxury goods could be obtained closer to the source, reducing the price for European merchants and increasing their profit margin upon delivery to Europe.
By: Cap'n Morgan