Before the voyages of exploration during this time period, Europeans had one option to get to the lucrative spice trade in the East—an overland route through what is now Russia and/or the Middle East. After the fall of Constantinople in 1453, the Ottoman Turks charged Christian traders high fees to get through. There were also marauding bands of Mongols and Tatars which regularly raided the trade caravans going through the Russian steppe. After Vasco da Gama found a way to the Indian Ocean around the tip of Africa, European monarchs were happy that they could get in on the spice trade while cutting out these interlopers. However, the trip was perilous given the weather conditions off the coast of Africa. Many Europeans speculated that one could reach Asia more quickly by sailing west. This led to further explorations by Columbus and the happy accident (at least for the Europeans) of discovering the Americas and the Caribbean.
Europeans were interested in finding a new route to Asia. The Europeans had a great deal of interest in trading with countries in Asia. There were many products that the Asians had that were in demand in Europe, especially spices. However, traveling the land routes to Asia proved to be very risky as traders had to travel through lands that were often disputed.
Vasco da Gama tried to find a new route to Asia by traveling by water south from Portugal around Africa to try to reach Asia. In 1498, he succeeded as he reached India. Christopher Columbus also wanted to find a new route to Asia. While he never did find a new route to Asia, he did travel to the Americas, which led to many other voyages to the Americas by the Europeans. The Europeans eventually set up colonies in the Americas.
During the time of Christopher Columbus, the route to India was very long and took a great deal of time which was costly in terms of the ship and the men who were paid to explore. Often, ships were lost at sea and the money invested lost as well. To find a shorter route to India and the spice trade would have made the discoverer and his supporters very wealthy. India was the source of so many spices which were worth their weight in gold that everyone was looking for that shorter route.
The flourishing trade between Europe and Asia happened only through land till the fall of Byzantine Empire. After the fall of Constantinople in 1453 the trade route was occupied by the Ottamans who levied very high trade taxes on the transit European goods to the east. Hence Europeans went on the quest of finding a sea route to Asia. Thus the Portuguese noble Vasco da Gama succeded in finding the sea route to India.
Now coming to why the seeked an 'alternate' route, the route that daGama found was insanely long with the ships having to sail around Africa then turn the course and reach Asia (Suez canal did not exist then). Moreover the sea route was very dangerous, the waters south of Africa (around the Cape of Good Hope) were turbulent almost althrough the year.
So Europeans were set on a new quest to find an alternate route. The earth is round. Hence an alternate route to the Orient should exist when you travel westward from Europe. Result!! Christopher Columbus set sail and stumbled upon the America instead of Asia !
Finding a new route to India (or to what was then called “The Indies” and is now known as Indonesia) was important during this time for economic reasons. A new route to India would be profitable for whoever found it. This is why Columbus was searching for such a route.
Trading with the Indies was very lucrative because the islands had spices. Spices were very valuable and could not be gotten anywhere else. The spice trade had to come overland and was dominated by the Muslims. Countries like Portugal and Spain therefore looked for routes to India, first around Africa and then, as with Columbus, through sailing west.