I am confused about this perk.

Does it make attacks while dual wielding faster, or do you have to press both mouse buttons at the same time, or does it make your dual power attacks faster?

I think it means you swing faster. I got it earlier today (only the first one) and I guess it seems like you swing a liiiiiiiiiiiiiiittle bit faster (20%)

edit: you still have to press left click then right click ect