Princess Aerea Targaryen was the daughter of Prince Aegon and Princess Rhaena Targaryen. She had a twin sister, Rhalla.
Aerea's parents were married in 41 AC. As this was an incestous marriage, this act led to a rebellion of the Faith. When Aerea's grandfather, King Aenys I Targaryen died, it was not Aerea's father, Aenys' eldest son and heir, Prince Aegon who was crowned king, but Aerea's great-uncle (and later step-father), Prince Maegor.
Aerea's father was killed in battle in 43 AC, leading to Princess Rhaena to go into hiding with both Aerea and Rhalla. They were eventually found, however, and captured on the orders of King Maegor.
Aerea's mother, Princess Rhaena, was forced to marry King Maegor I Targaryen in 47 AC. Because Maegor had no children of his own, Aerea was named his heir, while her uncle, Prince Jaehaerys was disinherited.
It is unknown what happened to Princess Aerea later in life.