The Siege of Vicksburg was important to the Union troops because they were able to take control of the Mississippi River. This allowed the Union troops to cut the Confederacy in half and allowed the Union to cut of supplies/resources to Confederate states.
The Battle of Gettysburg was an important Union win because this was the last time in the Civil War that the Confederate troops truly invaded the North. After this battle they did not invade any state north of Pennsylvania.
President Wilson’s approach towards the defeated Central Powers after World War I was to not punish them too harshly, since he knew this would only cause dangerous resentment. He did not get his wish, however.