What was the role of religion as a motive for American territorial expansion ?
Some individual colonies had restrictions on freedom of religion and thus some of the earliest motives for religious expansion had to do with the search for a place where people could practice their religion freely. Perhaps the clearest example of this can be seen in the migration of the Mormons to Salt Lake City. Originally, Joseph Smith founded Mormonism in New York. A key aspect of the religion was polygamy. To practice this, the Mormons first fled to Missouri and Illinois and then eventually to Utah, following the prophet Brigham Young. When they first saw the Salt Lake Valley, Brigham Young famously said:
"This is the place."
The Mormons then founded what became the Utah Territory and eventually the state of Utah. Another issue, more generically, was Manifest Destiny.