What is Nussbaum's conception of capability theory, and how does capability theory address the moral situations of women?

The "capability approach" is less of a crystallized theory and more of a loose framework of ideas about "well-being." Specifically, the approach seeks to 1) assess individual well-being, 2) assess social arrangements that promote well-being, and 3) design social policies that enhance well-being. Nussbaum in particular breaks down the approach to five principles:

treating each person as an end; a focus on choice and freedom rather than achievements; pluralism about values; being deeply concerned with entrenched social injustices; and ascribing an urgent task to government.

The capability approach intrinsically acknowledges diversity. In assessing well-being, for example, factors that affect women's quality of life that otherwise would be ignored are explicitly considered. Nussbaum's core capabilities explicitly make space for women's issues, casting them as fundamental human rights: these include bodily integrity, or being secure from assault, including sexual assault and domestic violence; the ability to use the imagination and engage in creative work; and the ability to have and sustain emotional attachments, free from fear and anxiety.
https://plato.stanford.edu/entries/capability-approach/