There are several reasons for this.

For one, there were two major theaters of war. They can be divided into smaller theaters, but for our purposes two theaters will suffice. There was the Eastern Theater, basically the Virginia, Pennsylvania, and Maryland area, and the Western Theater, generally Kentucky, Tennessee, and Mississippi. Remember, the U.S. is huge. Michigan alone is the size of the United Kingdom. The areas over which battles were being fought were massive.

We often talk about the "Union Army" or the "Confederate Army," but in reality there were multiple Armies. For example, in the Western Theater, U.S. Grant commanded the Army of the Tennessee (that is the Tennessee River). This Army fought in Tennessee at Shiloh and in Mississippi at Vicksburg before William T. Sherman took command and led them to the Sea. The other famous Union Army was the Army of the Potomac, led by George McClellan, Alexander Pope, George Meade, and finally led by U.S. Grant as General of the Army (though Meade stayed in command of the Army of the Potomac). There were lesser Union Armies, such as the Army of the Ohio, which fought at Perryville, and the Army of the Cumberland, which fought at Stones River and Chickamagua.

On the Confederate side, you had Robert E. Lee's Army of the Northern Virginia, Braxton Bragg's Army of Tennessee, and the Army of Mississippi, led by several different commanders.

Each of these Armies were made up of Corps, Divisions, and so on, like many world armies at the time, but an Army functioned as its own unit, moving in the field with a specific goal in mind. Grant's Army of the Tennessee for instance was tasked with breaking the Confederacy in half whereas the Army of North Virginia largely fought a defensive war, save one major invasion into the North.

Why is this important? Well, for one, it means that are numerous actions between the individual Armies. The Army of the Potomac fought the Army of Northern Virginia at the Seven Days Battles, Antietam, Fredericksburg, Chancellorsville, and Gettysburg plus other later battles. This was one Army maneuvering against another for years. Some battles even happened on previous battlegrounds. Cold Harbor was fought on the grounds of the Battle of Gaines' Mill, one of the Sevens Days Battles. There's a journal entry of a soldier at Cold Harbor finding bones from a soldier who died at Gaines's Mill.

Each Army had certain goals. The Army of the Potomac sought to capture Richmond, so there were battles around Richmond. The Army of Tennessee sought to split the Confederacy, so there were battles in the Western Theater seeking to meet this goal. All objectives were not met until 1865, so the war continued. Further, because of the locations of the objectives, soldiers were easy to come by.

The Civil War was a civil war. Soldiers lived around the battlefields. Soldiers were readily available and willing to fight. The American Civil War was not a war in a far off land. Rather, as ranks depleted, soldiers could be conscripted from just about anywhere.

Also, note that not every battle was battle like Austerlitz. The Battle of Wildcat Mountain in Kentucky had only a handful of causalities, but it is still considered a battle. In some cases, like the Seven Days Battles, you had 30,000 men in a single Army. Losses for a single army for a single battle might have been 3,000. They fought until they lost 1/3 of their strength, and then they would withdraw and regroup. Like Wildcat Mountain,though, not every battle was full scale assault. Some battles were mere skirmishes. Sometimes, like Rosecrans after Stones River, clever maneuvering prevented battles from ever being fought.

Further, remember that Confederates named their battles after towns whereas Union soldiers named battles after physical features. The Battle of Antietam was called the Battle of Sharpsburg in the South. A lot of major battles have two names, but they are not separate battles.

In conclusion, there were many battles because many Armies were fighting for objectives all over the United States.