Original: Christian later goes back to see Satine to convince her that she loves him ("Elephant Love Medley"). As the cabaret is converted to a theater for the show, Christian and Satine manage to continue to see each other alone, under the pretense of rehearsing Satine's lines.
Simplified: Satine confesses her love for him in the form of his secret song, and Christian and Satine get back together in full view of the audience and the Duke.