It all started in 1803 with the Louisiana Purchase. The Louisiana Purchase involved France selling French Louisiana, which was a very large section of the United States running across the North and South U.S. borders and the Caribbean too. It also included the New Orleans port. Total price was about $15 million dollars, but it covered over 828,000 sq miles of land (3 cents an acre). France, led by Napoleon, was having some real financial problems at the time, so I guess the deal made sense for them, but it sure seems like an unfair purchase today. Napoleon never even explored the area and did not realize how big the land was until after the sale was complete.
Once the purchase was made, it allowed the U.S. to declare the whole continent, from the West to East coast their own, which was a big achievement. However, nobody really knew much about it and many were afraid to even explore it. It was a big mystery. They had the "Wild West" on one side and the rest of the country on the other, but the Louisiana Purchase was an unknown chunk of land between them.
President Thomas Jefferson put the expedition together and Lewis and Clark led it with 45 other people. The focus was to explore the Missouri River with a goal being to allow for easy trade and colonization from the Pacific to the rest of the country. Thomas Jefferson thought the Missouri River connected directly to the Pacific Ocean, which is not correct since the Rocky Mountains divide it, which made the expedition even more difficult. It also was designed to help establish good relations with the Indian tribes and to collect, map and study information about natural resources and the unknown area in general.
