For a single action revolver, the hammer must be manually cocked which rotates the cylinder. Then the trigger is pulled, which fires a round. This must be done each time the shooter wants to fire a round.
For a double action revolver, the pull of the trigger cocks the hammer, rotates the cylinder, and fires the round. In addition, double action revolvers can be fired in the same manner as single action revolvers.
Usually, firing single action allows for a shorter trigger press and less pressure is needed to drop the hammer. Personally, I prefer this. It's nice to at least have the option. On my double action Taurus Judge, I like to shoot single action. Manually cocking the hammer and then squeezing the trigger gives me more control and much greater accuracy. This is true of most shooters. The fewer things i have to do, the more likely I am to stay on target and hit my mark.