Targaryens often had multiple wives. One of the biggest conflicts in Westeros was the Dance of Dragons that occurred 170 years before the start of the books. King Viserys I had two wives, the first wife was an Arryn and with her he had two sons and one daughter, the sons died as infants, leaving the daughter Rhaenyra the oldest progeny of King Viserys. King Viserys's second wife was a Hightower and she had two sons and two daughters, the oldest of the sons was Aegon II. When Viserys dies Aegon II becomes king (with the lord commander of the Kingsguard choosing Aegon as the true heir) and Rhaenyra starts a civil war claiming the kingdom should be hers. They fight and eventually Aegon wins and feeds his half sister to a dragon. Aegon reign was short lived for he soon after died having only a reign of 2 years (this time including the civil war). After Aegon's death Rhaenyra son Aegon the II nephew becomes king (who is known as Aegon the III)

Also Rhaegar Targaryen already had a heir with a son (Aegon) and a daughter (Rhaenys). Yet the siring of another heir was important to Rhaegar not due to needing another heir but his fascinating with prophecy and his belief that the dragon has three heads. He needed another child to fulfill that prophecy according to his beliefs and the sickness of his first wife made fufilling the prophecy problematic.

Now the death of Aegon, Rhaenys, and Elia at the hands of Gregor Clegane is a very important plot point. It caused Oberyn to champion Tyrion, and Oberyn and Ella's father Doran is plotting death to the Lannisters.