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.