Back outside, by his X-wing, Luke tells R2-D2 that he can't do it alone. Suddenly, the spirit of Obi-Wan Kenobi comes strolling through the woods. Perfect timing!
Obi-Wan backs up what Yoda said: Darth Vader is Luke's dad. He used to be a good guy, but the Dark Side seduced him, and when that happened, his old self (Anakin Skywalker) was destroyed.
Luke tells Obi-Wan that he thinks there's still good in his dad; Obi-Wan says he's more machine than man at this point. Also, as Anakin's personal Jedi trainer, Obi-Wan kind of feels like a failure.
Regardless, Obi-Wan says Luke still has to face Darth Vader. Luke says he can't kill his own father.
Then Obi-Wan drops another truth bomb: Luke has a twin sister. They were kept apart to keep them safe. The Emperor would see them as a massive threat since they were Anakin's kids.
Luke puts two and two together and figures out Leia is his sister. We can practically see the light bulb go off over his head.
Obi-Wan gives Luke one last piece of advice, telling him to bury his feelings. He's an insightful guy, but those feelings could be used against him by The Emperor, because The Emperor is one seriously evil dude.