What was Susan B Anthony vs. The United States of America about?

Women in 10 states voted in 1871 and 1872, in defiance of state laws prohibiting women from voting. Most were prevented from voting. Some did cast ballots.

In Rochester, New York, almost 50 women attempted to register to vote in 1872. Susan B. Anthony and fourteen other women were able, with the support of election inspectors, to register, but the others were turned back at that step. These fifteen women then cast ballots in the presidential election on November 5, 1872, with the support of the local election officials in Rochester.