In a way, the War of 1812 was a Second War of Independence of the United States from Britain, yet the circumstances were quite different from those of the Revolutionary War. This is why the title is a metaphoric one. Let's look at this in more detail.
Indeed, Britain did seem to have a difficult time getting used to the idea that it had no business sticking its nose into American affairs any longer. Of course, the US no longer had issues with Britain trying to tax its people or house soldiers on American soil after the Revolutionary War, but Britain did strive for authority it no longer had in more ways than one.
First, Britain was in a war with France in the early years of the 1800s, and it desperately wanted to cut off French supply chains. The French wanted to cut off British supply chains, too. Therefore, both sides tried to prevent the US from trading with their enemies. The British Orders of Council in 1807 required the US and other neutral countries to get a license from the British before trading with France. This, of course, far overstepped any power Britain had. The US was independent and did not have to abide by such restrictions. Yet the British stopped American merchant ships nonetheless to make sure their paperwork was in place.
What's more, when the British stopped those American ships, they sometimes “impressed” sailors from them, forcing them into service in the British navy. Sometimes the British claimed that the sailors were actually British deserters. Sometimes they didn't bother. This, of course, did not make the Americans very happy.
In these ways, then, the British were treating the US as if it were still one of its colonies, trying to control it and to make use of its citizens. The War of 1812 was fought, at least in part, as a result of these abuses, and therefore it can be called a “Second War of Independence” even though the title is metaphoric, since independence had already been won years before. Now it needed to be maintained.