What is so important about the Battle of Gettysburg ?
The Battle of Gettysburg was a major turning point in the war. It represented perhaps the last chance for the South to win the war in some way. If the South had won the battle, it might have been able to get European countries (particularly Britain) to recognize its independence and the war might have been over.
Gettysburg was part of an invasion of the North by the Confederacy. If the Confederate Army had been able to win major victories in its invasion of the North, the North might have had to give up the war. At the very least, such victories might have convinced European countries that the South would be able to hold its own and they might have recognized the South as an independent country. At that point, the North would have been in a very difficult position as Britain and other European countries might have started to put pressure on it to end the war.
So, the battle was important because it ended the Confederate invasion and, with it, the Confederacy's last major chance to be aggressive in the war.
The above response is absolutely rght. Gettysburg, had the South won, could well have been like the Revolutionary War's Battle of Saratoga, which convinced the French to enter the war on the American side.
The British were reluctant to back the South, given the fact that they had already abolished slavery and certainly did not want to aid its continuance in the US. However, a divided America offered some benefits for the British Empire, and with a southern win at Gettysburg, they may well have entered on the confederate side anyway.
In addition, it is important to note that the losses at Gettysburg, in particular on day three with Pickett's Charge, gutted the heart of Lee's Army of Northern Virginia (particularly in the officer ranks), and effectively ended their offensive potential. For the remainder of the war, they stayed in southern territory and remained a defensive force.