Say it is winter and the outside temperature is 0 degrees f.
I set my thermostat to 74 degrees. When the temperature inside my home reaches 72 degrees, the furnace will kick on and warm the house to 74.
Now, if I set my thermostat to 68 degrees to save energy, when my house reaches 66 degrees, the furnace will kick on and warm the house to 68.
In both instances, the same amount of energy was expended to raise the temperature by 2 degrees.
So how is it that keeping your thermostat at 68 will save energy?