The Dark Souls series is famous for its unforgiving difficulty, but not all the grief comes from within the world itself. Other players can invade your world, kill you, and totally ruin your day. Many Zelda games have you crossing blades with a dark, shadowy version of Link. This foe, cast in darkness and swirling shadows, is tantamount to an evil spirit invading Link's world. Just like in Dark Souls, when you see him standing across from you, you know that you're about to face an equal. Hell, the most recent Zelda title, A Link Between Worlds, actually takes this feature directly from Dark Souls, with other players sending their doppelgangers to attack.
The Dark Links that jump into Hyrule and challenge your Link are other player's avatars. They'll stand around your StreetPass tree and stalk the world's landmarks, daring you to challenge them. Once you enter into combat, you won't be facing off with an actual player behind the controls, but you still totally get that same need to rid your world of all invaders that you do in Dark Souls.