In the United States during the late nineteenth century, the women's movement was largely concerned with getting women the right to vote. These women were called "suffragettes," and they spent the 1890s, 1900s, and 1910s fighting for the right to vote in elections. Their goal was achieved in 1920, when the nineteenth amendment was finally ratified.

As the other answer mentions, the right to vote was about the only major right for women these female reformers supported that was women-specific. Otherwise, they were usually interested in the temperance movement, which saw alcohol as a major social evil. This related to women's rights in that many women saw alcohol as the cause of much domestic violence. Working conditions in factories and labor reform were also major concerns for women reformers.

The early twentieth century did see some women, such as Margret Sanger, arguing for the right to birth control for a variety of reasons, but this movement is linked with the 1910s, not the late nineteenth century.

Assuming that we are talking about women in the United States, the most important issue that faced them (that was directly tied to the issue of women's rights) was the desire for the right to vote.  At the end of the 19th century, women like Frances Willard were pushing hard for that right.

Most of the other issues that were of concern to women and to women's organizations like the WCTU were not directly connected to women's rights.  Instead, they were more generally progressive issues like temperance, federal aid to education, and labor reform.

Women who were politically active in the late 1800s were generally asking for one major right--the right to vote.  Outside of that, they were interested more generally in pursuing progressive reforms.