The significance of reading and writing in Jane Eyre lies in the fact that her education allowed her to move up in Lowood and eventually get hired as a governess at Thornfield (where she meets Edward Rochester, eventually falls in love with him,and marries him).
Without her education, Jane would not have become a teacher at Lowood. Without this prior experience, she (most likely) would not have been able to obtain the position at Thornfield.
On another hand, Jane's education is a very important characteristic in regards to Jane as a character. The fact that she is able to read and write proves her to be educated, some could say well beyond those of her peers. Therefore, her educated mind allows her to make very educated decisions (like leaving Rochester after she finds out that he is married). This essentially, proves her to be a woman who thinks with both her mind and her heart (given she does return at the end of the novel to find that Bertha Mason (Rochester's wife) has died and he is blind (showing the power of her heart).
Lastly, her education proves her to mirror those of aristocratic nature. At the end of the novel, Jane has been left a great sum of money. No longer does she have to live the life of the poor. Her education supports her societal stature at this point in the novel.