The Rebel Flesh is the fifth episode of the sixth series of Doctor Who. It stars Matt Smith as The Eleventh Doctor, Karen Gillam as Amy Pond, and Arthur Darvill as Rory Williams. It was the first of a two part story, with the second part being "The Almost People". The two episodes are an important part of the Series 6 story arc, but are also a stand-alone story.
SPOILERS!
Every series of Doctor who so far has had an episode treating a question of ethics, usually bioethics, and this is the Series 6 entry in that vein. In the 22nd century, the TARDIS materializes on earth, on a small rocky island that is involved in dangerous chemical manufacturing. So dangerous, in fact, that the workers do all their work via "Flesh" duplicates, basically organic robot duplicates controlled telepathically. But during a solar storm, the machinery of this "flesh" short circuits, and the duplicates develop a consciousness of their own, with all the memory and personalities of their original. The Doctor must sort out the thorny ethical issues, trying to get the humans and the flesh duplicates to come to peace with each other, while the plant fizzles and boils around them. It is a fairly classic Doctor Who story, combining aspects of the "Base Under Siege" story with ethical and political issues. It also has some great special effects, in the many scenes where one actor portraying both the original and the duplicate interact with each other.
After that is finished, we learn the arc significance of the story: The Doctor didn't come to the island by chance, but was in the process of researching the flesh technology, because he has guessed the strange status of Amy's pregnancy: her real body is pregnant, far away, while the Amy that we have been seeing for a while is actually a flesh duplicate. Her body melts away, and Amy wakes up, very far away and very afraid. Next, The Doctor and Rory will have to rescue Amy and their baby.