For the movie’s writers, the Nexus was first of all a device to avoid the expected mechanism of time-travel in getting Captains Kirk and Picard in the same place at the same time. But why “Nexus?” The word means a point or means of connection, and Braga and Moore said their original conception of it was as the place where past, present and future meet: the Nexus. But in the story, it is more like heavenly wish-fulfillment, a kind of super-holodeck (which may be why Picard is relatively quick to get outside its spell. He’s had lots of holodeck experience, whereas others—like Kirk—have not.)
The Nexus is apparently also a place to revisit your past starring roles. Picard turns out to be in the midst of a Dickensian Christmas (though the script etc. refers to it as a 24th century French Christmas, it’s clearly 19th century England.) Patrick Stewart’s celebrated one-man show was a version of Dicken’s “A Christmas Carol,” which led to a movie version. Later we will catch our first glimpse of Captain Kirk chopping wood—exactly as William Shatner is first seen in his starring role in Incubus (1965), one of the most unusual movies of all time, as the dialogue was spoken entirely in the artificial language of Esperanto.
Picard finds himself in what he recognizes as his home, surrounded by his wife and children—and his nephew, Rene—on Christmas day. He is dazed and dazzled and clearly “inside joy.”
Picard’s yearning for a family and the continuation of tradition that this scene dramatizes has been set up by the ready room scene, but for TNG fans it also has seven years of history behind it. In the TNG pilot, Picard confesses to Riker that he is uncomfortable around children. But over the years he develops a surrogate father-son relationship with Wesley Crusher (son of Beverly-- it turns out (in the 7th season episode "Attached") he’s been in love with her for years-- and of his best friend in Starfleet who was killed in the line of duty.) More specificially, he visits his family on earth directly after his assimilation by the Borg and rescue, and sees a kindred spirit in his nephew, who he calls "uncle" as a joke between them.
Then in an episode Picard is trapped in a turbolift with three children, and relates to them very well; they seem to have bonded by the end. In season 7, for awhile he believes that he in fact has a son and is trying to get to know him, before it turns out not to be true. Picard’s interest in history is also well-established in the series, and his ancestors become a plot point in the 7th season episode, “Journey’s End.”
But probably the most important backstory to this scene is what happened to Picard in the episode, “The Inner Light,” when an alien probe caused him to experience someone else’s life over many years, including the birth and nurturing of two children, and a grandchild. For the first part of this experience he retains a belief in his Picard identity, but it merges with the life he experiences, so when he admits that he once believed he didn’t need to have children to complete himself, but now he can’t imagine life without them—he is speaking as both Picard and Kamin, the identity he is experiencing.
But in the Nexus he can experience having a family fully as Picard, complete with connection to his Picard ancestors. There are even a portraits of them in this house, including one of the Picard who fought at Trafalgar (though presumably on the losing Spanish/French side), looking very much like this Picard in the holodeck sailing scene.
But this family is clearly idealized, and he has doubts (the twinkling of ornaments reminds him of the exploding star, or so the writers and director intended. I didn’t get it until I read about it.) Then Guinan appears (or her “echo” that remains in the Nexus) to tell him that anything he wants is possible, even leaving the Nexus. He asks for her help in going back and stopping Soran, but she suggests someone else.