Here is a little blurb I found on the Internet that does a fair job of summing up the history of the Mormon Battalion:
The Mormon Battalion Trek in 1846 consisted of over 500 men (and some of their families) who marched over 2,000 miles to help the U.S. government secure the state of California from being taken over by Mexico. It was a known fact that many of the men felt it wasn't their duty to help the government, as Mormons had not been protected by the government when they were persecuted and exiled from their own homes. At the Mormon Battalion Visitor Center, you will be able to learn about their hardships and experiences walking from Iowa to California--the longest military march in history. There are interactive exhibits, living history reenactors, and several films that take you back in time to walk a mile in their shoes and learn more about Mormon history.
And here is a link to an article with a more in-depth history of the Mormon Battalion.