Terror - the old tactic of 'monstering the tent' of your opponent when he cannot prevent you from doing so, so as to induce a feeling of impotence, which may well lead to his giving in.
It also sent a message across the South that the Union meant business, and would stop at nothing to end the war on its terms, and that the South could do nothing about it.
The swathe carved across Georgia also created the Civil War equivalent of a free fire zone, in which nothing grew and across which any movement would be plainly seen. It also divided the South in two, thus separating the Confederate armies in the north from much of their supplies. Although Union soldiers were not present in sufficient numbers to hold the entire area, neither were there sufficient Confederate soldiers available to throw them out.
The march through Georgia was also an outflanking movement, which forced the Confederate armies to face an enemy to both the north and the south at the same time, something they did not have the manpower or mobility to do effectively.
What a shame - it would have been nice to see that bastard Sherman hanged in Savannah.
It's about the destruction of the symbols of power .... by a power that is stronger.
Much like the destruction of the World Trade Centers in New York.
Also, with the plantations destroyed, the means of making money and re-gaining power were put to an end.
Any wealth and/or power would have to be completely rebuilt over a period of time.
Things would be forced to be done in a different ways.
The old ways of doing things that caused problems to begin with were all gone.