It's used to good effect on birds with patterns. It would only be used if you wanted to maintain a cockerel and a pullet line.
Good quality of both sexes can be maintained with one line but usually smaller breeders just maintain a pullet line.
Barred birds would be easy to explain why double mating is advantageous. Males carry two copies of barring resulting in a pale looking bird as the black barring line is thin. These are the males you'd see in a pullet line- a line that expresses best color in pullets. These males couldn't compete in a show and are not quite to standard as the cock and hen should look similar.
As stated you can breed for both sexes looking to standard and achieve good results but nothing like you would breeding for pullets only or for cockerels only.
I think the concept of double mating is clear now. I'll just finish up the mating of barred males. A male line of barred is one that breeds for males with wider barring. This will make the bird look similar to the pullets. To achieve it the darkest females are bred. Continually doing this would create a cockerel line. Little chance of obtaining a good looking pullet from it, the line is bred only for high percentage of correct pattern cockerels.