In many wars of the past, the fighting went on even after the war was over. Most of these can be attributed to slow communication. Before telegraphs and telephones, it could take weeks to get a message anywhere, and the difficulties were only greater during wartime. But that wasn't the only reason the fighting didn't stop. Sometime it was hard to define when a war "ended."
The Battle of New Orleans is often remembered as one of the most decisive American victories in the War of 1812. It’s also often remembered as an infamous battle-fought-after-the-war-ended, though the moniker is only half true. It’s true that the battle, which was fought on January 8, 1815, took place after the Treaty of Ghent was signed in Belgium on December 24, 1814, and even after the treaty had been ratified by the Prince Regent (the future King George IV). But President James Madison and the American Senate did not ratify the treaty until February 16, allowing the battle to assume an arguable level of tactical importance.
The Battle of New Orleans is only one of eight such battles explained at mental_floss. Link