Why did nations want to find a northwest passage?

The East had many rich things - spices, silk, and so on. But, to get them to markets in Europe was very difficult. The "Silk Road" had many warlords, each demanding taxes (tribute), and there were many bandits. Sailing all the way round Africa, and to the Orient was exceedingly difficult in 1500 - still is in fact.

The NorthWest passage offered a short cut. It is the same today - the trip is considerably shorter, and that mean the companies could become very rich a lot easier. In theory - they never found a good route, and even today with Global Warming opening it up, it is still a difficult route to sail.