The two battles that are most often cited as turning points in the Civil War occurred at the same time. These were the Battles of Gettysburg and Vicksburg, both of which occurred (or ended) in July of 1863. Gettysburg lifted Northern morale by inflicting a major defeat on General Robert E. Lee, who had seemed invincible. It also ended the Southern invasion of the North, robbing the South of any leverage it had to force the North to make peace. Vicksburg was important more for geographical reasons. It allowed the North to control the entire Mississippi River. This cut the western Confederate states from the eastern states. It also allowed the North unlimited use of the rivers to ferry supplies and men. For these reasons, these two battles are typically cited as turning points.
Some historians call Gettysburg the turning point. I think there was no turning point.
The North cut the South into pieces. Taking and holding New Orleans and Vicksburg cut Texas from the fight. The advance from Shilo to Atlanta cut off most of the rest of the South. With Northern armies on the north and the south of Richmond, Virginia could not continue.