The Gadsden Purchase was intended to

Slightly expand the territory of the United States in order to allow a southern transcontinental railroad to be built more easily without having to go into Mexico or through the Blue Mountains of Arizona, which are significantly harder to put railroads through than the relatively flat desert that takes up most of the Gadsden Purchase. There was also a fair amount of copper, gold, and silver there, although they didn't realize this until after the purchase. America also got Tucson out of the deal, so there is that.