Some Reasons:
Europeans had begun to demand valuable goods such as silk and spices that could only be found in Asia, and also European merchants had manufactured goods to sell in Asia but needed a way to get them there.
Why:
Europeans wanted valuable goods like silk and spices. But these goods were only found in Asia. Europeans needed a sea route so they won't have to just explore to try to find their way to Asia. Kings especially wanted these nice goods, so they really wanted a sea route then.
European merchants manufactured goods to sell in Asia. But if they wanted to manufacture the goods, they would have to have a way to get there!
