The story follows five major "fish out of water" sub-plots:
* The bridge is isolated from the rest of the ship and the watch officer is killed in the collision. This leaves Counselor Troi in command - as a lieutenant commander, she is the highest ranking officer left alive on the bridge. She is assisted by Chief O'Brien and Ensign Ro.
* Captain Picard is in a turbolift with three of the children of the ship's crew, who have won a school contest to meet him for a tour of the ship. When the disaster hits, they are trapped in the damaged turbolift; Picard suffers a broken ankle.
* Doctor Crusher and Lieutenant Commander La Forge are in a cargo bay discussing La Forge's possible participation in a ship production of The Pirates of Penzance. A minor radiation leak from a plasma fire threatens to destabilize a large quantity of an explosive thruster-fuel compound.
* Worf and a pregnant Keiko O'Brien are in Ten Forward (which Riker has organized as a medical center) tending to the injuries of the crew when Keiko goes into labor.
* Commander Riker and Data, unable to contact the bridge and assuming no one is in control, attempt to reach engineering to regain control of the ship.
Several characters are developed in this episode, but arguably the one given most focus is Troi. Although her command is unchallenged, she faces constant pressure from Ro to cut loose the drive section (whose warp core is becoming dangerously unstable) to save the saucer section. Conversely, O'Brien wants to do anything possible to save those still alive in the drive section. (This heavily parallels a typical Spock-McCoy argument.) Troi is clearly handicapped by her lack of technical knowledge, but eventually manages to assert herself in order to give the crew in the drive section a chance. This experience later lends weight to her decision to become a full commander, a goal she achieves in a later episode.
In this episode, Picard also deals with his discomfort in relating with children. As a child, Picard was consumed by work - both in his family's vineyard and winery, and with his own studies to meet his dream of becoming a starship captain. His own childhood lacked a sense of fun, immaturity, and emotional response, and since most children have these qualities, he has difficulty dealing with them. In previous episodes, we have seen him banning children from the bridge, and expressing extreme discomfort when dealing with the emotions of children - even normal displays of affection. At first, he attempts to be authoritative - his usual response when people around him panic. However, this only makes the children more upset. Eventually, he makes a game of escaping the crippled turbolift, "promoting" the children with honorary Starfleet ranks, and even engages in a children's song to take their minds off of the dangerous climb up the turbolift shaft. At the end of the episode, he is clearly far more comfortable with the children, having spent more time with them and learning how to relate to them.
When Keiko goes into labor, Worf's response is cynically comical ("This is not a good time!"). However, although he is clearly uncomfortable in the role of midwife, and having only basic medical training in the subject, he delivers a healthy baby girl - the O'Briens' child, Molly Miyaki Worf O'Brien.
La Forge and Crusher manage to kill two birds with one stone - briefly depressurizing the cargo hold to both expel the dangerous cargo and rob the fire of oxygen. However, the epic maneuver threatens both with asphyxiation.
Riker and Data suffer a number of difficulties trying to reach engineering. At one point, Data's body must be sacrificed as an insulator to block a rogue electric current; only his head survives. However, on reaching engineering, they find only one operable console and discover that it is being fed power from the bridge (thanks to Troi's decision to route power there). They realize the antimatter-containment system is weak, and Data manages to re-establish it just in time.
The episode ends with the Enterprise crew en route to a nearby starbase for full repairs after having made basic repairs. It shows Data back at his post with his body repaired. The three children who had been trapped in the turbolift with Picard present him with a plaque; the episode ends as Picard promises the children a tour of the battle bridge, which he had earlier told them was off-limits.