Under Jefferson Davis, the Confederacy opened fire at Fort Sumter when Lincoln sent a peaceful expedition of supplies to the cite, and won the battle. It is significant because the battle was the first shots of the war.
Battle of Forts Jackson and St. Philip, LA (04/18-28, 1862)
The Union launched a marsh against the Confederate capital Richmond, but was stopped by General Jackson at Bull Run and defeated by a strong counterattack. It is significant because it made the North realize the war would be much more difficult and arduous than imagined, and General Jackson got the nickname "Stonewall."
Second Battle of Bull Run, VA (08/28-30, 1862)
The battle was one of the Confederate attempts to break the Union blockade of water. It ended in a draw. It is significant because it was the first meeting in combat of ironclad warships.
Battle of Antietam, MD (9/17, 1862)
Lincoln set in motion an Army-Navy combined attack of New Orleans from the South and successfully took the city from the Confederacy. It is significant because North gained control of New Orleans, the single most important city of the South.
Jackson led Lee's campaign against Union general John Pope, captured the Union supply, devastated a Union assault and defeated them with big casualty on both sides. It is significant because the Union army was defeated in the same place for a second time but of larger scale and numbers, showing the South's strategic advantage.
McClellan led Union army to launch attacks at Lee's Confederacy army behind Antietam Creek, ended up defeating Lee with a shocking amount of casualties. It is significant because it was the bloodiest single day of the war with 22717 dead, wounded, or missing.