Luke: "I will not fight you, father." Darth Vader: "You are unwise to lower your defenses!"
Darth Vader: "Give yourself to the Dark Side. It is the only way you can save your friends. Yes, your thoughts betray you. Your feelings for them are strong. Especially for... sister. So, you have a twin sister. Your feelings have now betrayed her, too. Obi-Wan was wise to hide her from me. Now his failure is complete. If you will not turn to the Dark Side... then perhaps she will..."
Luke does not want to fight his father, Darth Vader, so Vader starts to use Luke's feelings against him. He senses that Luke feels strongly for his sister and suggests that, if Luke won't go to the Dark Side, then maybe she will. This finally gets Luke going.