For the first time, Rhaegar Targaryen made an appearance on Game of Thrones and fans were excited to finally see him. However, although Rhaegar's name has been dropped a few times over the course of the show, there's still a lot viewers don't know about him. So what happened to Rhaegar on Game of Thrones? His actions launched the start of a rebellion.
Rhaegar was the eldest son and heir to King Aerys II Targaryen, also known as the Mad King, making Rhaegar, the Prince of Dragonstone, the Targaryen's family stronghold. Originally, Tywin Lannister hoped Cersei would be the one to marry Rhaegar and become queen, but the Mad King refused that proposal. Instead, he had Rhaegar married off to Princess Elia Martell of Dorne, his distant cousin. (In case you were unaware, the Targaryens are kind of into incest.)
Once Rhaegar and Elia were married, they then had two children: a daughter named Rhaenys and a son named Aegon. In the books, during the great Tourney of Harrenhal, Rhaegar caused issues when he won the contest and gave the victor's wreath, known as the Queen of Love and Beauty, to Lyanna Stark, instead of his wife. This was very problematic because Lyanna was betrothed to Robert Baratheon at the time; and when Rhaegar and Lyanna later disappeared together, it was assumed that Rhaegar abducted her.
Because of this, Lyanna's eldest brother Brandon went to King's Landing to get his sister back, but the Mad King imprisoned him. When Brandon's father arrived to save him, the Mad King then burned them both alive, a story Jon recounted to Daenerys when they first met. This led to Ned joining up with Robert to overthrow the Targaryens in what became known as Robert's Rebellion. At first Rhaegar stayed away from the fight, choosing to be with Lyanna in Dorne, but he was eventually forced to join the fight. Robert then killed him during a duel.
In the Season 7 finale, it was revealed that Rhaegar didn't actually abduct Lyanna. The truth was they were in love and ran off to be together. Rhaegar had his marriage to Elia annulled and he then married Lyanna, who later became pregnant with his child. That child is Jon Snow, whose real name fans just found out is Aegon Targaryen — the same name Rhaegar give to his first son who was killed, along with his sister and mother, during Robert's Rebellion at the hands of Ser Gregor Clegane.
Because Jon is the son of Rhaegar, he is actually the heir to the Iron Throne, not Daenerys. Thus, once this information is revealed, it could potentially change everything for both Jon and Dany.