The Empty Child/The Doctor Dances is a two part story of Doctor Who, and was the 9th and 10th episode of the first series of the Doctor Who revival. The Doctor in the series is The 9th Doctor, portrayed by Christopher Eccleston. Since I take the division of the story into episodes to be an artifact of the medium, this write-up will cover both of the episodes.
The episode is considered by many to be one of the more significant and better episodes of the Revival of Doctor Who, an opinion that I share, although it was only after I viewed it that I started realizing how much skill had been placed into the characterization and plot of the story. A brief synopsis of the plot will be described, before I explain why this particular story was so important in setting the tone for the Doctor Who revival.
The Doctor and his companion, Rose Tyler, find a lost vessel in the time vortex, and trace it back to 1941 London. The Doctor and Rose get separated, and Rose meets Captain Jack Harkness, who will later become a very important figure in Doctor Who, and its spin-off, Torchwood. Meanwhile, The Doctor has stumbled upon a mystery, in the form of the titular Empty Child, a boy in a gas mask who stumbles around, asking the same question: "Are You My Mummy?" A teenage girl, who seems to know a little of what is going on, warns The Doctor away, although that of course does not dissuade him. The Doctor later rejoins Rose and Captain Jack Harkness, and finds out that Captain Jack is an time traveling con-man, who crashed a piece of what he thought was space junk into the earth, then sells its location to "Time Agents", but that he had made a mistake: what he thought was an empty ambulance actually was full of "nanogenes", nanotechnology meant to heal injuries. The nanotechnology had found a boy killed during the blitz, and not knowing what humans were meant to be, had taken him as a template, and then moved on to infect other people, thinking it was "curing them" by rewriting them into the form of the injured boy with a gas mask. The Doctor realizes that the teenage girl who he had first met, who warned him about the boy, and claimed it was her little brother, was not telling the truth: actually, she had been a teen mother, and the boy was her son. When she embraces the boy, the nanotechnology recognizes her as a parent, and gets a proper fix on what a human form should be. The infection of all the other people were reversed, and the Doctor joyfully yells "Everyone Lives!", and the two of them rescue Captain Jack, and then travel on further in time.
I realize that synopsis is both too short and too long, although those familiar with Doctor Who and its plotlines will recognize a vintage quality Who mystery, and those not familiar with Doctor Who...will not be reading this.
But even all that plot is just the dressing on what this episode is really about, which is sex. The second episodes title, "The Doctor Dances", seems to be somewhat of a non-sequitur, until the equation between dancing, sex, and the themes and events of the episode are made.
Doctor Who is, in many ways, an escapist show, and The Doctor is an escapist character. He is aloof, superior, always has the answer, and has powers that are, despite the science-fiction trimmings, more or less magic. He also is rarely rattled by what goes on around him. And while the Revival has in many ways continued with the show being an escapist fantasy, it also has allowed some character development. The Doctor is often above humanity, but he also is lonely and needs companionship. He shows his affection by protecting and helping people, but he is unable to gain personal satisfaction from it, especially in light of the guilt he has from having to watch people die, and sometimes being responsible for it. At the climax of the story, he tells Rose to watch his "dance moves" and blows the nanogenes towards the crowd of zombified people, restoring them to health. In other words, he blows out genetic material to give life --- certainly a sexual metaphor. The girl who is the hidden mother of the injured boy is also in denial of her sexuality, dressing and acting like a girl on the edge of puberty, and denying the consequences of her sexual activity. Her admitting that the child is hers is the key to unlocking the entire mystery. And then, of course, we have Captain Jack. Captain Jack has the opposite problem as The Doctor: while The Doctor is all caring, and no sensuality, Captain Jack is all sensuality, with very little responsibility. In another fairly obvious innuendo, the episodes problems start because Captain Jack is irresponsible with a large cylinder full of genetic material. At the end of the episode, in another very, very obvious innuendo, he appears with a large bomb between his legs, which was originally part of his con. However, he takes responsibility for the bomb, meaning he has learned to temper his sensual nature with maturity.
So this episode, in a very encapsulated and subtle form, introduces many of the basic character conflicts that would become important as the Doctor Who revival progresses. The author of this story, Stephen Moffat, would later become the chief writer and show-runner. The story first sets up the conflict between The Doctor as aloof, all-powerful and celibate hero, and the Doctor as guilty, lonely man who needs companionship but has a difficult time obtaining it. It also, with Captain Jack, introduced the idea of a character that is a foil to The Doctor, whose impulsiveness, selfishness and sensuality can form a good pair with the Doctor's introverted and cerebral nature. A similar character would later be introduced by Moffat, the Doctor's (possible?) wife, River Song.