The Campaign For Chattanooga:
After the firm possession of Nashville early in 1862, and the subsequent battle of Stones River, December 31, 1862, and January 1 and 2, 1863, the objective of the Army of the Cumberland was Chattanooga.
Chattanooga was the gateway through the Cumberland Mountains for the Union Army to the Atlantic seaboard States. For the Confederates it was a railway center of immense importance. It occupied the intersection of nearly all their trunk lines. Those from Richmond through East Tennessee to New Orleans there crossed the lines from Memphis to Charleston, and those from Kentucky through Tennessee and Georgia to the Southeastern seaboard. There was only one other line of communication between Richmond, Atlanta, and New Orleans.
See blog post Securing Lookout Valley.