Some historians have called the War of 1812, the Second War of Independence. There is some credence to this as the combatants were the same and the country was at stake. When the War of 1812 is called the Second War for Independence it is with a little bit of short-sided wishful thinking.
The truth is, the War of 1812, was America's largest military blunder until the Vietnam War. The fact is the United States lost the war, militarily speaking. When looking at the war, from 1812-1815, the United States only had two successful years. 1812 was successful from the Navy side, while 1814 was successful from the Army side. 1813 and 1815 were militarily disastrous for the United States. This was in large part because the war hawks in Washington (Republicans) decided that invading Canada would not only be successful, but that the Canadians would be very happy to see us come in. The Federalist Party (which was very much on the way out the door as a political party) did not have enough members to stop that course of action.
The United States did win on one front and it was the most important front. The country won the battle of diplomacy to end the war. Interestingly enough, the Federalists had argued for diplomacy before the war ever started. It turned out that they were right. In Washington, however, where the party that is the loudest usually wins the PR war, the Republicans got out in front and declared that they had won. By 1820 the Federalists were no longer a party, by 1823 the United States had moved into the Second Americans Party System and the Republicans were also gone.
The War of 1812 had many important points. During the war, saw the only time in history that Washington D.C. was ever held by an invading army. It also saw quick thinking by Dolly Madison and the Postmaster General for D.C. to save many of the country's documents. It also saw the beginning of American dominance at sea and the beginning of the end of England's dominance at sea. It also saw a general rise to prominence and eventually win the presidency (Andrew Jackson) based solely off a huge military victory, after the war had ended (The Battle of New Orleans).
Next year marks the 200th Anniversary of the War of 1812 and one thing that all historians and politicians can agree on is that there is no direct answer to the question "What was the importance of the War of 1812?"