That date seems a little early for women's suffrage doesn't it. You're probably thinking... the 19th Amendment wasn't passed until the 1919. You're right. But March 8, 1884 marks the first date that Susan B. Anthony argued before congress. It was on this date t hat she began her address before the Judiciary Committee of the House of Representative.
We appear before you this morning…to ask that you will, at your earliest
convenience, report to the House in favor of the submission of a Sixteenth
Amendment to the Legislatures of the several States, that shall prohibit the
disfranchisement of citizens of the United States on account of sex.
Arguing to amend the Constitution to allow women the right to vote, Anthony was finally given the floor sixteen years after the idea for women's suffrage was introduced in Congress. So those that were thinking, this was a little early, must now realize that indeed it was a little late.
Anthony addressed the House Committee for four days, but it would take 35 more years before Congress would approve women's suffrage. On June 4, 1919 the "Anthony Amendment" was finally approved. On August 18, 1920, the states ratified it as the Nineteenth Amendment to the Constitution. However what was originally proposed as the 16th Amendment from Anthony took so long to pass, it was now the 19th Amendment.
Unfortunately, Susan B. Anthony died in 1906 having never cast a vote and never seeing the fruits of her labor. For more information about Women's suffrage and Susan B. Anthony, visit The Susan B. Anthony House: http://www.susanbanthonyhouse.org/
Here's a timeline from the Library of Congress charting the women's suffrage movement: http://memory.loc.gov/ammem/vfwhtml/vfwtl.html
And for those that really love research and primary source documents, the Library of Congress Manuscript Division has a collection of the Papers of Susan B. Anthony: http://www.loc.gov/rr/mss/text/anthony.html