The expansion of the US population in the years after 1812 was to have a huge impact on Native American populations. In general, it pushed them out of their own lands and then out of the lands that had been given to them when they were removed from their original homes. It ended up causing them to be isolated on relatively small reservations that were often in very inhospitable areas.
After 1812, America acquired areas like California and Oregon. The overland trails (and eventually railroads) to these new acquisitions helped also to bring more Americans into the area acquired in the Louisiana Purchase in 1803. As more and more Americans moved into these areas, Native Americans were displaced. For some, this meant being displaced from areas where they had been sent during the Indian Removal of the 1830s.
Eventually, this expansion led to a situation in which Native Americans were largely confined to reservations in out of the way areas that were least useful to white people.