How exactly does Akiko's healing ability work?
Akiko explain's her own ability when she is on the train with the bomber in episode 8 at 16:45.


  "My ability, Thou Shalt Not Die, can cure any wounds. Even my own injuries as you can see. But the necessary conditions are harsh. It can only cure lethal injuries. What an inconvenient ability. If I want to cure moderate injuries, I have to half kill my patient first." - Akiko Yosano


From the wiki:


  Akiko has a rare ability among ability users, Thou Shalt Not Die (君死給勿, Kimi Shinitamō Koto Nakare?), which allows her to heal external wounds. However, to heal someone they must first be "half-dead"; meaning they must have fatally serious injuries before she can use her ability. Due to this, her ability is inconvenient for healing minimal wounds since she needs to fatally injure that person first.


As for Akiko's name. She was named after the feminist poet Yosano Akiko. Yosano Akiko's poems were written during the Russo-Japanese war which was around 1945 when feminism wasn't highly thought of. The early-to-mid 19000s in Japan was a time when women were slowly gaining new rights, during this time feminism was a huge thing for women, but controversial overall.

You could say that Akiko's nature and appearance embody this ideal.