A star whale was a giant, space-borne cetacean.
Star whales were sentient and were similar-looking to Earth's cetaceans in basic structure. They had several flippers and tentacular protrusions down their stomach, as well as smaller, spiked tendrils on their back. Star whales travelled through space at speeds comparable to spaceships. Though they could communicate in an atmosphere, their voices were too high-pitched for humans to hear. They were capable of bioluminescence and had glowing patterns around their tendrils. (TV: The Beast Below)
They fed on solar power from the stars they passed. They would occasionally eat humans, but refused to harm children. Their intelligence was higher than that of humans and they could live for thousands of years.
By the 29th century, the species was believed extinct save for one individual. When Earth faced destruction because of solar flares, that star whale was drawn to Earth. All the peoples of Earth had escaped in massive city ships, but the people of the United Kingdom lacked an engine. The star whale intended to offer its services to the stranded people as it sensed the terror of the children and, being so old and kind, could not bear to see them cry.
Unfortunately, the people of the UK misinterpreted this gesture of good will as a lucky coincidence and captured it. They built their ship on its back and carved an opening to its brain to torture it into moving. The city built on its back became known as Starship UK. While the government realised the moral problem, they believed that if the whale was freed, Starship UK would be destroyed, killing the population. To deal with this, every five years they revealed the truth to citizens one at a time and allowed them to vote on the matter, choosing either to "Forget" or "Protest". Forgetting meant their memories would be erased so they didn't have to live with the guilt. However, protesting meant that particular citizen would immediately be fed to the star whale. Every year the overwhelming majority of citizens chose to forget. Similarly, Queen Elizabeth X (Liz Ten for short), whose body clock had been halted and who had ruled the British people for three hundred years, was faced with the choice to Forget or Abdicate every time she found out the truth. Abdication would free the star whale, but as previously stated, it was believed that this would destroy the Starship UK.
When the Eleventh Doctor and Amy Pond came to Starship UK in the 33rd century, they investigated the ship. Along the way, Amy stumbled into a voting booth and learned the truth, only to vote to Forget. Eventually the Doctor discovered the heart of the ship, where Hawthorne and his workers were torturing the star whale with electric shocks to keep it moving, and faced the impossible situation. Seeing no reasonable options, the Doctor tried to render the space whale brain-dead so it would no longer feel pain from the torture, but would continue to support the ship. Amy, however, noticed the whale's neural tendrils affectionately playing with the children. She quickly put the pieces together and ran to the control system to press the "Abdicate" button with Liz Ten's hand, freeing the whale.
The ship was not destroyed as was originally feared. Instead it started to move faster. As the star whale had come willingly and was still willing to help the people of the UK, it moved more swiftly without the torture dulling its senses. Amy explained her reasoning to Liz Ten, Hawthorne and the Doctor, comparing the star whale's situation, being "very old and very kind and the last of its kind," to the Doctor himself who, like the star whale, could not bear to see children in distress. (TV: The Beast Below)
After being sent back in time by the Weeping Angels, Amy Pond used the afterword of Melody Malone's book, "The Angel's Kiss: A Melody Malone Mystery", to tell the Eleventh Doctor to tell her younger self "she'll save a whale in outer space", as a reference to the star whale. (TV: The Angels Take Manhattan)