On its way to help an ecologically devastated planet, the Enterprise-D picks up a clever young intern, who reveals for us her secret power of making puppies appear from nowhere.
Amanda (played with an impressive mixture of maturity and teenaged vulnerability by Olivia D’Abo) chats with Dr. Crusher about family, and we learn she was adopted as a baby.
Right before a cargo container falls on Riker, she deflects it with a gesture. Later, in engineering, the warp core suddenly acts up and explodes, but she manages to reverse the explosion and restore the ship.
Q suddenly appears, saying that Amanda’s parents were members of the Q Continuum who took on human form, and had a child. Although Amanda appears completely human, she seems to have inherited her parents’ powers, and so Q is here to train her and take her back with him.
Crusher objects to the whole scheme, but Picard reluctantly agrees to introduce Q to Amanda, who resists Q (actually tossing him across the room) and remains attached to her goals of joining Starfleet and living a normal human life. To get her to use her powers, Q encourages her to conjure up a memory of her parents. (This scene has a lot in common with Harry Potter sadly looking at his parents via the Mirror of Erised.)
Amanda is committed to doing routine tasks for Crusher, but Q manages to get her to practice her teleportation powers by playing hide and seek; a stunning scene has them standing on the exterior hull of the ship, with the stars above them.
At dinner with Troi and Crusher, Amanda says she’s starting to enjoy using her powers. When Riker stops by to say hello, Amanda awkwardly invites him to join them, but Riker has other plans — a date with someone at another table. This makes Amanda jealous, and in a flash, she and Riker are in a gazebo dressed like characters from a Jane Austen novel. When she forces Riker to play the lover, the fantasy is an empty disappointment for her.
We learn that Q’s real mission is to decide whether to invite Amanda into the Q Continuum, or to kill her.
After a break to develop the B plot of the ecologically devastated planet, the story returns to Picard giving another impressive monologue about human morality. Q scoffs, but reveals a third option — Amanda can continue to live her human life if she refrains from using her Q powers. (Did Q listen to Picard and soften his views? Will Amanda be able to keep her promise?)
Almost immediately we get a call from Riker — down on the ecologically devastated planet one of the eco-fixing machines is on a countdown to certain destruction.
This sci-fi B-plot fits neatly into the climax of the character-based fantasy/magical/supernatural A-Plot.