Literally, Bertha Mason is a very real impediment to Jane's marriage to Mr Rochester. Since he is still married to her, his marriage to Jane cannot progress as planned.
As a metaphor, Bertha represents the gothic element in the novel - wild, dark, closely related to nature. In addition, we can also see her as the 'madwoman in the attic.' This is a concept that was developed by Sandra Gilbert and Susan Gubar in their 1979 book examining Victorian literature from a feminist perspective. This work suggests that madness in Victorian writing was often an analogy for rebellion and anger against the restrictions placed upon women in the home and in public. The result of this for Jane is that it forced her from Thornfield, gave her the opportunity to re-discover her family, stand as an independent woman and not marry just because it was offered to her. When she returned to Rochester, it was on her own terms.
Bertha Mason adds to the element of the gothic that Bronte infused into this work and adds a plot complication that sustains the reader's interest in Jane Eyre's journey to self-realization. If Jane could have simply married Rochester, the story would be over, and Jane would have been the obediant wife. However, it is through Jane's heartbreak that her character strengthens. She becomes stronger than Rochester, and the balance in their relationship shifts. Jane becomes the independent, triumphant heroine who is able to carve a path in the world on her own while Rochester is both physically and emotionally destroyed. Rochester becomes dependent on Jane. If it were not for the horrors of Bertha Mason, Jane's journey to selfhood could not have taken place.
The most straightforward answer would, of course, be that Bertha delays Jane's marriage to Rochester and sends Jane on a journey where she will meet the Rivers family. Many critics see the figure of Bertha, however, as far more complex than a simple barrier between the hero and heroine that must be overcome. For example Gilbert and Gubar's classic essay on Jane Eyre claims that Bertha serves as an "avatar" for Jane, someone who does what Jane herself really wants to do but cannot. One of these actions might be when Bertha destroys Jane's bridal veil.