It emphasizes Jane's autonomy as an individual.
Autonomy implies the ability to be strong enough to be on one's own.
In terms of being strong enough, Jane:
Her ability to stand on her own is expressed by such phrases as "I must and would be alone."
It signals that Jane is shifting away from reliance upon St. John.
The first sentence of the excerpt clearly states this claim, especially its first part: "I broke from St. John."
Other phrases expressing her leaving St. John behind include: