The significance of Lincoln's switch from using the term "union" to "nation" was that in doing so he was attempting to redefine the whole concept of American nationhood.
In his First Inaugural Address, it's instructive that Lincoln used the word "union" over and over again but never once used the word "nation." Yet by the time he came to give the Gettysburg Address in 1863, he referred to the new nation brought forth by the Founding Fathers.
The term "union" implies a collection of states, all bound together by a common commitment. Clearly, such a concept was untenable after a number of Southern states seceded and formed the Confederacy.
In the union's place, Lincoln posited the notion of the nation, governed by a strong central government based on popular sovereignty—government "of the people, by the people, for the people"—that would bring about
"a new birth of freedom."
Here Lincoln was heralding the transition from one form of government—a collection of states—to another one, a modern, unified nation governed by a powerful federal government.