Board Thread:FAQs/@comment-29313623-20180812234833/@comment-4010415-20180817000714

His Semblance amplifies Aura, according to the writers.

Basically, Aura can naturally accelerate the healing of minor wounds, but Weiss' wound was major, not minor. So, he amplified Aura's ability to accelerate the healing process, making it more powerful and allowing Weiss' wound to heal enough for her to live.

The reason that it's so important to note that Jaune has a lot of Aura is because he has to use a lot of his Aura to do this, so if he had a normal amount, he would run out quickly and put himself in danger. But since he has a lot, he can use his Semblance more than someone else would, if they had his Semblance.