In the early years of the Church, for spiritual and physical safety and to strengthen the Church, the saints were commanded to gather with the main body of the Church. This both served to strengthen the individual and the Church as a whole. Gathering started in New York, then moved as the Church moved . . . to Ohio, Missiouri, Illinois, and finally Utah.
The early Saints mostly gathered from Europe, particularly Great Britain and Scandanavia. They gathered from Australia as well and from several places in the United States. Many converts became great leaders in the Church.
After the main body of Saints arrived in Utah, Brigham Young established a perpetual emigration fund. Members donated to the fund to help other Saints gather to Utah. These Saints were expected to donate the amount they received to emigrate back into the fund, when they could, although not everyone was able.
Immigration to Utah didn't necessarily mean immigration to Salt Lake. Many Saints were called to settle throughout Utah, Colorado, Arizona, Nevada, and California, as well as parts of Canada and Mexico.
Gathering became less of an emphasis from the late 19th century on. The US Government passed laws which made immigration more difficult. Saints were asked to stay in their own lands and build up the Church there. The blessings would remain the same.
Today, temples are built all over the world and there are more members outside the United States than inside, although many members do still immigrate to the United States for many different reasons and are welcome to. Gathering, however, no longer serves an active purpose in the Church and staying in one's home country is still encouraged. In an area conference in 1972, Bruce R. McConkie said the place for Saints to gather was in their own countries. This was reaffirmed by Presidents Harold B. Lee and Spencer W. Kimball.