Before 1920, women did not have the right to vote in the U.S. The suffragist movement fought for these rights, and the people who were part of that movement were suffragists.
The word suffrage means the right to vote in elections. It does not have to do with suffering. In America, the individual states determine who may vote. However, the U.S. Constitution states in the 19th Amendment that women shall not be denied the vote based upon their sex. Suffragists fought hard to bring this constitutional amendment about. Back then, female suffragists were known as suffragettes.