A family from a long time ago in a galaxy far far away that has a reputation for fucking everything up and everyone feels that the galaxy would of been better off if they never existed
Similar to the Oedipus complex, where Oedipus sleeps with his mother without actually knowing they are related, the Skywalker Complex is named for Luke Skywalker after kissing his sister, before learning that they were related, in The Empire Strikes Back. The Skywalker Complex is used to describe anyone who has "a thing" for a sibling.
Joe: "Dude, that girl is pretty hot."
*Girl turns around*
Ben: "DUDE THAT'S YOUR SISTER!!! Hahahaha, man you have such a Skywalker Complex!"
Joe: "Not fair I didn't know it was her!"