Who is the woman marching across the plains supposed to represent?

Manifest Destiny

Explanation:

Assuming you're referring to the 1872 painting 'American Progress', where a woman in white is crossing the plains alongside pioneers and Natives, the woman represents Manifest Destiny.

This is the idea that God deemed the American nation to be worthy of conquering the continent and spreading their civilized, superior culture, ideals, government, and society from the Atlantic to the Pacific.

what the first or next guy says

a.  

women in ancient egypt had many legal rights, including the right to own property and businesses.