1. Her Goodbye
There are a lot of ways to say goodbye on Doctor Who. Weve seen each companion offer a farewell to the Doctor over the years. Weve watched him exchange final words, give and take final requests, and hold off the end as long as he can for as many people as he can manage. How we face our endings defines us in many ways, so how Clara faced her death is essential to understanding her character. She decided that her life was worth the Doctors, that she was willing to die to save him, because she could. She had a chance to save him, and she took it. It wasnt, as some people have said, an agencyless time-paradox decision (as so many of Rivers were). And her different lives spread across time and space may have been created in order to save the Doctor, but this act didnt limit her. Her choice to leap into the vortex and save the Doctor again and again was an act of love which elevated her, which made her bigger. And her goodbye was pure Clara. A set of orders, and a pet name, made up possibly the most important sentence of her life. She didnt cry, or hesitate. She didnt do what Rose would have done, and swear undying love. She just told him to run and remember her. Then she got on with it.
To Conclude
There has never been a companion quite like Clara. Her fierceness, her spirit, and her clear-sightedness set her apart from every other character who has ever occupied her position. No one else has quite understood the Doctor like Clara does, has viewed him with the clear lens she sees through.
I love River, but she once referred to the Doctor as an immortal god. Phrases like that are not good for the Doctor because he might start believing them. The Doctor needs companions who drag him out of that god-mindset, who see him as a man first and a time lord second. He needs people who have faith in him as a man, and nothing more. Thats why he needs Clara so much. And thats one of the many reasons why shes awesome.