The lesson of the cutscene is "It will rain Ilias."
Also, "Don't do drugs."
But, yeah, in all seriousness, it's what others have already conveyed - it was meant to be a lesson in history and a warning about the seduction of power told - in a dreamlike fashion - with figures closest to Link. Seeing strife between a figure looking like himself and one looking like his best friend/possible village crush was a good way of showing the concept of "betrayl" - how power made the early people of Hyrule betray one another. Then the Dark Links were representative of the Dark Interlopers (the Twili ancestors), seduced by power/giving into their darksides. Also, Dark Link is an inexplicably popular character in Zelda-fandom, so it looks like Nintendo just crammed the Dark Link concept in there as a bit of non-sexual fanservice.