Madison Picard was the daughter created by the Nexus for Jean-Luc Picard as part of a representation of his own ideal life.
In this representation, she was the youngest daughter of Captain Jean-Luc Picard and Elise Picard, created as part of an ideal fantasy by the Nexus. She had two elder sisters, also created by the Nexus, Mimi and Olivia. In the short time Jean-Luc Picard spent inside the Nexus, Madison opened Christmas presents and sat ready for dinner, before Picard decided duty was more important then fantasy, and continued his mission. (Star Trek Generations)
Madison can be seen at three distinct times inside the Nexus. She is the only girl directly holding hands with Matthew Picard, played by actor Matthew Collins, running out to greet their father, Jean-Luc Picard, for the first time in the Nexus. She is also the young girl being held by her mother Elise Picard, played by Kim Braden. And, finally, she is the young girl seen with her back to the camera at the Christmas dinner table.