Whether you're talking about America the continents or America the modern country, the answer is a variety of reasons.

The Spanish, for example, were looking for precious metals and Catholic converts. Among the English colonies there was huge variation in reasons for going to the New World. The Puritans in Massachusetts sought to create a religious utopia based on the tenets of their relatively small movement in England. Virginia was settled by English aristocrats who wanted to recreate the hierarchical society of England and make big money of tobacco plantations. The common initial motivator for setting up colonies was economic gain, but these secular ventures were often co-opted by people with religious agendas willing to actually go out into the wilderness and create new societies.

No empire was interested in creating a new nation. In a perfect world, conquered territory would be populated by the same people as in the home country and would be instantly loyal to their occupying overlord. If the two test choices were "religion" or "new nation" I'd go with religion, but in the end I think "money" beats them both.

Good luck!