It came from an episode of Big Bang Theory; when Penny gets hurt, and asks Sheldon to be more comforting, he starts the conversation with "there, there."
What does that mean?
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The Wiktionary explains it in the best way possible:
there, there: (idiomatic) Conveys comfort; used to calm somebody or urge somebody to relax, especially when the person is crying.
There, there. Even though you broke up with her, you'll be fine.
The phrase "there there" you basically use, when you are consoling or trying to console someone (especially a kid ) with "there there" you are insuring the person everything is alright. For example: A kid has lost his favorite toy and starts crying. Mother: " there there....we'll get you a new one"