There are two main ways in which the Lewis and Clark expedition impacted the development of the West.
First, the expedition made traders and trappers more interested in the West. The expedition brought back reports that convinced the traders and trappers that there was money to be made by trading with the Indians or by trapping furs on their own.
Second, the expedition and the reaction to it helped to give the US a claim to the Oregon country. Since Americans were the first to extensively explore the area, they had a strong claim to it. This helped the US get Oregon in the 1840s, thus helping to ensure a stream of pioneers heading west.