Why did american business seek new markets in the early 1900's?
In a nutshell, new markets meant more money. Because of industrialization, America was producing more than it could consume. Rather than allowing the excess to become waste, it is a wiser investment to expand your market. Mass production is far more profitable as the expense of making the product is less.
In addition to selling our goods to others, we also needed their resources. Dominating an area where there is an abundance of natural resources, allows our companies to produce items at an even lower price.
Prior to the 1900s, Americans would not have been able to produce enough to satisfy the needs at home and abroad, and the transportation of goods/resources would have been slowed down immensly before the creation of the Panama Canal.
There are at least a couple of important reasons for this.
First of all, businesses are just about always seeking new markets. That is just what businesses do.
Second (and this is probably the more important one for your answer), businesses in the US were becoming more and more industrialized and mechanized. This meant that they could produce more goods than they used to using the same number of workers. Because of this, they now had all the ability to produce more (perhaps) than the domestic market could buy up. This led them (some say) to push for new markets. This push is said to be an important reason for the imperialism of the early 1900s.