He was trying to find a quicker, more efficient way to Asia to trade with the Chinese, because the route that was currently being used was long. He didn't know about the Western Hemisphere (the one with North America), and people recently accepted the fact that the Earth was round, so he thought it would be a quicker trip. He ended up finding the "New World," instead of Asia, but regardless, he was convinced he found Asia, even when he died.
Hope this helps! :)
