Jason's whole character arc centers around the question "Who is Jason Grace?" At the start of the TLH, even Jason doesn't know the answer to that question as the series progress he starts gaining some parts of his memories.
While he is gaining his memories, we(the audience) learn more facts about his life too. We learn that Jason has been raised as a soldier, he has been at Camp Jupiter for years. He is expected to be the perfect roman, the perfect soldier.
Then we watch as Jason tries to gain a new identity away from all of the expectations. He tries to become something other than a champion of Juno, he tries to be something other than a soldier.
And for a while he manages to escape his soldier status. He leaves Camp Jupiter, has a (semi)stable relationship with Piper, has new guardians(Mellie and Coach Hedge), has his friends etc.
After a while, he and Piper broke up. Mellie and Hedge blame Jason for the breakup so he moves to an all-boys boarding school. Then he and Piper go into the Labyrinth, here Jason learn that either he or Piper has to die.
In the end, he dies in a quest and his character arc comes to an end as the audience finally recieves an answer to the "Who is Jason Grace?" question.
The answer is that Jason Grace was a soldier who was born to die for the gods from the very beginning. Him trying to gain another identity aside from Juno's champion was pointless from the beginning. He was meant to be a hero that died for the Gods, his fate was sealed the day he became Juno's champion.
His story ends with his body being brought back to Camp Jupiter, the place that raised him to be the perfect soldier.
















