Why the U.S. Conquered an Empire:
I think the two answers already given are good ones, except that one point is stated backwards. The desire for empire was the reason for the development of more military and naval power, not the other way around.
The big businesses desired captive markets, and closely controllable sources of resources such as bananas from Central America, a captive market in the U.S. sphere of China, cheap labor from the southern states of the U.S., and more. Some places were captured primarily for their usefulness as naval bases to defend the empire, Midway being one such. Hawaii had strategic location, a great harbor, pineapples, and plenty of American businessmen and pineapple planters already living there.
The idea of the white man's burden was easy to believe, since expansion of empire to facilitate it would reap economic profits. I wonder if the American empire was ever expanded into areas where no economic profit was to be made, just to bring civilization to the natives. (?)
Manifest Destiny - our belief as a people that God wanted the US to expand from coast to coast - had been completed by 1848, and in the half century afterwards, the land had been explored, settled and the resources exploited or claimed. Now what was big business and the Gilded Age robber barons going to do next to make another fortune and keep their prosperity going?
The various motivations listed in pohnpei's post are right on the money, and I would also say that the economic benefits of becoming an empire in the late 1890's was the primary driving force behind our doing exactly that.
A variety of things did.
First, the desire for more military power. The US thought they should have naval bases around the world so as to be more of a world power.
Second, economic power. They wanted to have the ability to trade with a lot of places -- get raw materials, have captive markets.
Finally, the idea of the "white man's burden." Americans thought the US should go and civilize the non-white people.
All three of these had something to do with imperialism -- you can argue about which one or ones was more important as a motive.