The following is from a work-in-progress called The Qur'an: a Book Report, in which I read each surah of the Qur'an and write about what I learn.
This surah is interesting from a women's rights perspective because it actually asserts more rights and protections for women than previously existed in pre-Islamic times. Thus, it goes against popular stereotypes that Islam and the Qur'an are totally misogynistic. In some ways, as this surah shows, the Qur'an was extremely progressive for its time.
In pre-Islamic Arabia, men who wanted to divorce their wives could do something called Zihar, in which they said to their wife, "Thou art to me as the back of my mother." This freed the husband from marital responsibilities, but it did NOT free the wife. She still had to stay in the husband's home and could not re-marry. This surah abolishes that practice.
The context for "The Dispute" is that a Muslim man said to his wife the Zihar, thus divorcing her in the traditional way. The woman then complained to Muhammad that this was totally unfair. The prophet's response was to abolish the practice, in the name of fairness.