Not just hindu women, but specifically the wife of the dead man on the pyre.

Sati was a daughter of the sage Daksha. When she came of age, her father organized a svayamvara, an event where the best and the brightest young men come and do all they can to impress the young lady, who has to choose her groom.

Daksha invited all the gods to his daughter's svayamvara, except Shiva, because he hated Shiva. The day progressed, the Gods performed many miraculous feats, and the time came for Sati to choose.
Sati was in love with Shiva, and none of the acts performed by the other gods had caught her eye. She walked around the meeting hall carrying a garland, and directing her thoughts toward Shiva. Sati threw the garland up in the air, as an offering to Shiva, who appeared below the garland. After Shiva caught the garland around his neck, Daksha had to accept him as a son-in-law. But, he didn't have to like him.
Knowing his father-in-law's distaste for him, Shiva didn't try to get on his good side, in fact, it might be said that he did the opposite. Once, when Daksha entered a room where Shiva was sitting, and Shiva did not get up to greet him.
Daksha held a sacrificial feast, and did not invite his daughter's husband. His daughter, outraged and horrified, built a sacred fire and threw herself into it. She burned up.
Since this event, Sati has become a term used for the self-immolation of a wife or a widow.