"Ender's Game" was originally a short story by Orson Scott Card. He later fleshed it out into a full-length novel and followed it up with a number of sequels, Speaker for the Dead, Children of the Mind, Xenocide, Ender's Shadow, Shadow of the Hegemon, and Shadow Puppets. It is the original Ender's Game novel that has the most enduring popularity at CTY, though the sequels are also generally appreciated.
Ender's Game tells the story of Ender Wiggin, an extremely precocious 5 year old, who is trained by the World's government to become a military leader in the war against a dangerous alien threat, the Buggers. Ender meets all expectations and at the age of about 10 leads Earth's forces against the Buggers, only to be confronted with the realization that the battle he fought might not have been his.
The book is one of the Things we like, probably because it depicts a host of young geniuses who as a result of their intelligence feel out of place in society. The Battle School might be considered an analogue of CTY, raising important ethical and social questions about the nature of the people who emerge from the CTY program. To CTYers, in short, Ender's battle is our battle.
But Ender truly did achieve a great victory, and in being finally given a challenge worth fighting, he grew up into an adult. Ender's struggles after battling the Buggers show that he has evolved from a child's black and white view of the world to a far more gray-shaded understanding. We might mourn the premature loss of Ender's innocence, but CTYers know what it's like to lose your innocence early, and the resulting struggle has its rewards as well as its downside.