After learning from a young Enterprise resident named Clara that she has an "Invisible friend," Troi reassures the girl's father, Daniel Sutter, that the practice is normal. Since Clara has been moved from starship to starship, Troi explains that her imaginary friend "Isabella" provides her with a constant companion. Meanwhile, the Enterprise investigates a rare nebula that has formed around a neutron star. As the exploration proceeds, a strange energy source makes its way onto the ship and begins to conduct an exploration of its own. The being discovers Clara playing in the Arboretum, and immediately materializes into the image of her friend Isabella.
Clara is astonished to see her imaginary friend come to life. Isabella convinces the girl to take her on a tour of the ship, concentrating on forbidden areas like Engineering, the Bridge and the Ten-Forward. The crew is shocked to see Clara popping up in such unexpected places, especially when she blames her "companion" Isabella, whom none of the adults can see. At the same time, Picard and the crew are troubled by mysterious energy strands which have surrounded the ship like a web and are causing it to lose power.
Troi decides Clara should meet some other children, and arranges for her to attend a ceramics class. The girl immediately hits it off with Worf's son Alexander, that is, until Isabella arrives and destroys one of Alexander's creations. Since Alexander can't see Isabella, he blames Clara. Later, a tearful Clara confronts Isabella, asking why she has been so mean to her. Isabella coldly replies that when the "others" come, Clara and everyone else on the ship will die.
Terrified, Clara confesses to her father that she is afraid of Isabella. Sutter calls Troi in, and the counselor accompanies the little girl back to her room to assure her that she is safe. She looks under the bed and in the bathroom in an effort to prove to Clara that nothing is lurking in the shadows. However, when she opens the door to Clara's closet, Isabella appears before her and knocks Troi unconscious with a strand of red energy.
Making a connection between Isabella and the beings that are draining the ship's energy, Picard begins a search for the girl. He finds her with Clara's help, and she tells them that she was on board to assess the ship's energy sources. When Picard tells her there are ways of providing her race with energy without destroying the ship, she replies that she plans to destroy it anyway. But when Clara asks her to spare them, Isabella changes her mind. She dematerializes, and moments later, the energy strands vanish. Picard orders Geordi to drive the warp engines to full power and direct the energy into the nebula, providing the aliens with the needed nourishment. Later, Isabella says goodbye to Clara in her quarters, and the two pledge to always remain friends.