Very simple.Single action means you must pull the hammer back (cock it) then squeeze the trigger to fire it.
Double action means you can fire it as discribed above or you can just squeeze the trigger and it will bring the hammer back then fall to fire.For target shooting most shoot Single action.For self defense D/A,is quicker and prefered for self defense.Squeezing the trigger on a D/A has a heavier trigger pull,then does a Single Action.

Ruger Redhawk