The war of 1812 was considered the United States' "Second War of Independence". Because the U.S. was able to withstand one of the greatest military powers of the time, the British Empire, it gained the respect of many foreign nations. This also led to the raising of US citizens' morale and general sense of nationalism.
Also, the professionalism of the US military increased substantially during the war. One key part to this increase in professionalism was the improvement of officer training in the United States Military Academy.
These increases of morale and power would make the United States a stronger and more united nation.
After the war, the Monroe Doctrine was added to U.S. foreign policy. This stated that European nations could not colonize any part of the Western Hemisphere. If they were to attempt to expand from their current colonies or their homeland, it would threaten American security. The Doctrine also threatened retaliation if any European powers did try to expand into the Western Hemisphere.