Why was it important for the union army to capture the city of atlanta?

According to Grant's strategy, it wasn't important at all.

As General-in-Chief, he was not interested in capturing territory, only in destroying the Confederate armies, wherever they might be.

Sherman's orders were to target Joe Johnston and the Army of Tennessee. But when they got out of Atlanta and headed for the mountains, Sherman did not succeed in capturing them.

So he decided to occupy Atlanta instead, realising that it would sound like big news in the North and help Lincoln's re-election chances.