Shipping furniture is different from using a mover. A shipment of furniture goes by truck, as freight, and needs to be packed accordingly. It also takes longer to ship furniture than to use a mover.
When should you ship furniture? Sometimes, you may want to send pieces to someplace other than the place you're moving -- for instance, if you're moving to Ireland and you want to send Grandma's antique desk back to your mom's house in Kansas. Another example might be for an overseas move, though unless you are planning to resettle permanently it might be cost-prohibitive to ship all but a few very treasured items.
See tips on "Freight Shipping" for more about choosing a freight carrier and packing your shipment.