Drogon is the largest and fiercest dragon in all the world during the events of A Song of Ice and Fire. He is the black dragon of Daenerys Targaryen's flight. In the previews for A Dance with Dragons, it is revealed that Drogon killed and ate a child. When Dany locked her dragons away to keep her people safe, Drogon flew away to the Dothraki sea.
When he was born, many of Dany's followers believed him to be the second coming of Balerion the Dread, the largest and most powerful of the Targaryan dragons of ancient times. Daenerys then believed it would be suiting that she give him a new name to both honour the dead and give him a new chance in life.
He seemed to appear to Dany at some points before his birth in dreams during A Game of Thrones. The first time he seemed to appear in her dreams prior to her wedding to Khal Drogo and shortly after her brother Viserys had beaten her, towering over Dany before she awoke from fright. When she was having difficuly adapting to her role of Khaleesi, even going so far as to contemplate suicide, he again appeared, towering over her again and covered symbolically in Targaryen blood. He stares Danerys down before dousing her in fire, "cleansing" her of her old life.