An important conference is to take place on the planet Pacifica and the USS Enterprise-D is ordered to escort two Antedean ambassadors to the conference. The Antedeans (one of whom was played by Fleetwood Mac member Mick Fleetwood), who look like fish walking on two legs, arrive in a self-induced catatonic state in order to avoid the stress from the journey. When they awake, they will be extremely hungry, which is why they brought a large can of their favourite food, vermicula, with them.
En route to the conference, the Enterprise-D encounters a Federation shuttlecraft carrying the Betazoid ambassador Lwaxana Troi, mother of Counselor Deanna Troi. Lwaxana Troi insists on coming aboard the Enterprise-D for the rest of the journey, so she and her mute manservant Mr. Homn are taken aboard.
What the crew of the Enterprise-D doesn't know is that Lwaxana Troi is in "The Phase": a stage in the life of a middle-aged Betazoid woman when her sex drive more than quadruples. Long-since widowed, Troi is eager for a new husband. She starts her search with Captain Jean-Luc Picard, but when he invites Data to their private dinner in order to trip up Troi's game, she goes on to other candidates. She strongly considers Commander William Riker, but her daughter dissuades him. She also considers Rex, the bartender from Picard's Dixon Hill holodeck program, but Picard later informs her that he is not real.
Right before the conference, the Antedean ambassadors awake and gobble up their entire supply of vermicula. However, when Lwaxana Troi meets them, she immediately reveals them to be assassins, intent on blowing up the entire conference with a lethal supply of ultritium. The assassins are arrested, and Troi departs to the conference, saying that if she did not manage to find a new husband, at least she saved the conference.