Ser Arthur Dayne is famous for his ancestral sword Dawn, forged from a falling star, in the books. In the show some fans were upset that he was shown with two swords (which did include Dawn.) Showrunners made the decision to give him two swords to make Dayne look epic, as he was supposed to be the best swordsman in the realm at the time. 

"We were looking for something that Arthur Dayne could do that would exhibit almost superhuman prowess. While we tried, we could not achieve that using one sword," director Daniel Sackheim said on Reddit.