An important conference is to take place on the planet Pacifica and the Federation starship Enterprise, under the command of Captain Jean-Luc Picard, is ordered to escort two Antedean ambassadors to the conference. The Antedeans are transported aboard in a self-induced catatonic state to avoid the stress from the journey. When they awake, they will be extremely hungry, which is why they brought a large container of their favourite food, vermicula, with them.
En route to the conference, the Enterprise encounters a Starfleetshuttlecraft carrying the Betazoid ambassador Lwaxana Troi, mother of ship's counselor Deanna Troi. Lwaxana Troi insists on coming aboard the Enterprise for the rest of the journey, so she and her mute, towering manservant Mr. Homn are taken aboard, much to the annoyance of Picard (and others).
What the crew of the Enterprise 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 quadruples - "perhaps even more", as Deanna discreetly informed the senior staff, to which the First Officer, Commander William Riker jokingly replies it "will be interesting", earning him a muffed chuckle from Deanna and an uncomfortable glare from his captain. Being long-since widowed as well, Lwaxana is now eager to find a new husband and sets her sights on the men aboard the starship. She starts her search with Captain Picard, but when he invites his androidSecond Officer Data to their private dinner to trip up the elder Troi's game, she lets Picard go and moves on to other candidates. She strongly considers Riker, albeit rather to tease her daughter, who nevertheless vehemently dissuades her (and unintentionally confirms she still has strong feelings for him). She also considers Rex, the bartender from Picard's Dixon Hill holodeck program (where Picard hoped to hide from her, in vain), but Picard, albeit somewhat reluctantly, informs her that he is not real, much to Lwaxana's own disappointment and embarrassment.
Meanwhile, and almost right before the conference, the Antedean ambassadors awake and gobble up their entire supply of vermicula. However, when Lwaxana Troi meets them shortly after, she immediately senses something amiss, and reveals them to be assassins, intent on blowing up the entire conference with a lethal supply of ultritium, hidden within their supply. The assassins are arrested, and Ambassador Troi departs to the conference, saying that while she did not manage to find a new husband, at least she saved the conference. Shortly before beaming out, she playfully chastises Picard for having "such naughty thoughts" about her, leaving the captain feeling even more uncomfortable than when she was around.