Set in the 24th century, the series follows the adventures of the crew of the Federation starship Enterprise-D. In this episode, as the crew of the starship Enterprise struggle to prevent a moon from falling out of orbit, their situation is further complicated by a visit from a powerful nemesis named "Q" (John de Lancie), who informs them that he has been stripped of all his powers and must live out a mortal life.
The Federation starship Enterprise arrives at planet Bre'el IV to prevent the looming disaster of the planet's asteroidal moon falling from its orbit and crashing into the highly populated planet; as the ship arrives, the planet is already experiencing damaging effects of the moon's gravitational field. As the crew is working, Q (John de Lancie) appears on the bridge naked. Q explains that after he lost the wager with Captain Picard (Patrick Stewart) regarding turning Commander Riker (Jonathan Frakes), he has been stripped of his powers, banished from the Q Continuum, and transported to the Enterprise as a human, asking asylum. Picard respects Q's wishes to be treated like a human and throws him in the brig.
As the moon continues to descend to the planet, Picard suggests that Q assist the Engineering team. Q suggests that they "change the gravitational constant of the universe." Experiencing hunger for the first time, Q goes to the Ten-Forward lounge with Commander Data, who suggests a chocolate sundae. After ordering ten sundaes, his hunger is quickly displaced upon encountering Guinan (Whoopi Goldberg), who takes advantage of Q's mortal form to stab him with a fork. Shortly thereafter, Q is set upon by a cloud of gaseous entities called the Calamarain, who, having previously been tormented by Q, are attempting to get revenge. After raising the shields to prevent the Calamarain from attacking Q, Picard determines that Q took refuge on the Enterprise to protect himself from alien species that hold a grudge against him.
Q's idea of manipulating the gravity field of the moon sparks an idea in Chief Engineer La Forge (LeVar Burton), which he tests; however, the test lowers the Enterprise 's shields, allowing the Calamarain to attack Q again. Data attempts to prevent their assault but is charged with electricity, nearly frying his positronic brain. Realizing that his presence on the Enterprise is doing more harm than he expected, Q leaves the ship in a shuttlecraft. As the Calamarain close onto the shuttle, a second Q being (Corbin Bernsen) appears on the shuttle and informs Q that the Continuum is willing to give him a second chance and restore his powers. Q accepts and shrinks the Calamarain entities and teleports them into the palm of his hand, gloating over the restoration of his powers. The other Q reminds him that he should reflect upon the lessons he's learned, and he grudgingly turns the tiny aliens loose. Q returns to the Enterprise and celebrates. Nudged by Picard to leave, he departs, bestowing a parting gift on Data for showing him how to be human. After Q disappears, Data begins to laugh uncontrollably for a moment, to the surprise of the rest of the Enterprise crew. Upon learning that the Bre'el moon has returned to a safe orbit, Picard surmises that Q is responsible, and says that perhaps Q has a residue of humanity after all, but an image of Q appears and tells Picard, "don't bet on it."