At the start of 1863, Robert E. Lee's Army of Northern Virginia had been frustrating the Union in the Eastern theater for several months, but the situation in the West was completely different. The Confederates had lost control of several important states throughout 1862, and after New Orleans was taken by the Union, the North controlled almost all of the Mississippi River, which Confederate general James Longstreet called "the lungs of the Confederacy." By taking control of that vital river, the North would virtually cut the Confederacy in two, putting the South in a dire situation.
The only domino left to fall was the stronghold of Vicksburg, and both sides knew it. The Union Army of the Tennessee, led by Ulysses S. Grant, would spend months trying to force John Pemberton's Confederate army to surrender. Grant eventually succeeded on July 4, 1863, but since it came a day after the climactic finish of the Battle of Gettysburg, Vicksburg was (and still is) frequently overlooked as one of the turning points of the Civil War. In fact, had the Confederate's military leadership listened to Longstreet, who advocated detaching soldiers from Lee's army to head west and help the Confederates deal with Grant or Rosecrans in that theater, the Battle of Gettysburg might never have happened.
While many read about the siege of Vicksburg in the summer of 1863, as well as the desperate straits the Confederate soldiers and Vicksburg residents found themselves in, Grant's initial attempts to advance towards Vicksburg met with several miserable failures, and it took several months just to get to the point where the Union forces could start a siege. First, Grant's supply base at Holly Springs was captured, and then an assault launched by Union General Sherman at Chickasaw Bayou was easily repulsed by Confederate forces, with serious Union casualties resulting. Grant then attempted to have his men build canals north and west of the city to facilitate transportation, which included grueling work and disease in the bayous.
On April 30, 1863, Grant finally launched the successful campaign against Vicksburg, marching down the western side of the Mississippi River while the navy covered his movements. Realizing Vicksburg was the objective, the Confederate forces under the command of Pemberton gathered in that vicinity, but instead of going directly for Vicksburg, Grant took the state capital of Jackson instead, effectively isolating Vicksburg. His forces won a couple of battles outside Vicksburg at Champion Hill and Big Black River, forcing Pemberton's men into Vicksburg and completely enveloping it. When two frontal assaults were easily repulsed, Grant and his men settled into a nearly two month long siege that ultimately won the campaign. It was the largest troop surrender during the entire Civil War, and Vicksburg's residents were so embittered that popular folklore maintained Vicksburg didn't celebrate Independence Day for a generation.