While the Enterprise is en route to pick up samples of various viruses for study to assist with a plasma plague, a strange, glowing light covertly comes aboard the ship. After floating around for a bit and inspecting a couple of rooms, it enters Counselor Troi, who wakes up, mildly distressed.
Meanwhile, the new Chief Medical Officer, Dr. Katherine Pulaski, has come on board. Dr. Crusher departed between seasons to become head of Starfleet Medical, and Wesley will shortly be leaving the Enterprise to join her. When Picard discovers that Dr. Pulaski is in 10- Forward without having reported in yet, he goes to find her. When he arrives, Pulaski (who's just been talking to Troi) sits him down, and tells him exactly what he tells the rest of the crew at the staff meeting: Deanna is pregnant, and the pregnancy is proceeding at an extremely rapid rate. After some discussion about what's to be done, Deanna states that she's keeping the child no matter what.
The ship reaches Odett 9 to pick up the samples. The medical trustee there, Hester Dealt, comes up to inspect the containment field that new Chief Engineer La Forge has designed, and sends along a manifest of all the samples that are to be brought aboard. Several hours later, Troi delivers her baby-with no pain, and little effort. She names the child Ianandra, after her father. The next day, Picard goes to pay his respects, only to find that Ian is now physically almost four years old-and he can even talk.
After the manifest is inspected (and Pulaski warns Picard of just how nasty these specimens are), the samples are beamed aboard, and the Enterprise leaves for Rachelis. Ian, by now, is physically and mentally about eight, and seems obsessed by new sensations and feelings. When asked if he's ready to tell everyone why he's come, he says merely, "No-not yet."
Suddenly, Dealt and Geordi detect growth of one of the organisms. There are no problems in the containment field, however, and they can't explain it. Furthermore, if growth continues, there's no way the Enterprise can prevent being completely overrun. They eventually determine that the growth is being stimulated by Eichener radiation, but are at a loss to figure out what's emitting said radiation. Ian, realizing it's him, tells Troi he must leave, and "dies", turning back into the glowing light we saw earlier.
It converses telepathically with Troi, telling her that it came to learn about humanity, and took human form to do so. With the radiation gone, the samples quiet down again, and are delivered safely. Finally, Wes decides he wants to stay on the Enterprise, and after conferring with the bridge crew, Picard gives him permission to do so.