To frighten citizens in Georgia so they would give up on the cause of the Confederacy.
General Sherman's "March to the Sea" was a march of a fighting force of around 60,000 men, going from Atlanta to Savannah, Georgia (a distance of 285 miles). It was intended as a show of force, to intimidate. They did not burn everything in sight, but did burn the houses and barns of any people who tried to resist them or fight back.