He simply means that those who died at the Battle of Gettysburg gave their lives to save the Union. For Lincoln, that was the whole point of the Civil War: not to end slavery, but to keep the Union together, to prevent it from breaking apart. Lincoln famously stated that he would tolerate the existence of slavery if it meant that the Union remained intact. For him, as for many in the North and Mid-west, this was the most important thing.

Later on in the speech, Lincoln goes on to elaborate on his remarks concerning the Union war dead. They died to keep the nation from breaking apart; they've done their part. But now it's the responsibility of the living to finish what Lincoln calls the "unfinished work which they who fought here have thus far so nobly advanced." This means that Americans must continue to devote themselves to the cause for which so many brave men perished at Gettysburg: a new birth of freedom.

In the early part of his speech, Lincoln refers to the men of Gettysburg dying so that the nation might live. Towards the end of his speech, there's a subtle change corresponding to Lincoln's change in attitude towards the War's fundamental goal. The war dead didn't simply die to save a Union, but a specific kind of Union, a Union founded on a "new birth of freedom."