According to Women's History at About.com, women were not allowed to vote because it was thought that women were not concerned with politics; and, they were already represented by their husbands. Historically, women's roles were in the home, as wives and mothers, not as citizens who engaged in politics. Wikipedia explains that women's active participation in World War I helped earn them a right to vote.
When the 19th Amendment to the United States Constitution was passed, in 1920, it officially gave women the right to vote. The campaign for women's suffrage, however, began almost 100 years earlier. While women's suffrage gained momentum with the help of abolitionists, the outbreak of the U.S. Civil War in 1861 caused the movement to stall. According to History.com, concentrated efforts were made in favor of granting citizenship and voting rights to black males at that time.
History.com states that in 1890, the National American Woman's Suffrage Association was formed with Elizabeth Cady Stanton as its first president. In 1910, many western states began joining Utah and Idaho, which had given women the right to vote at the end of the 19th century: But states in the South and East continued to resist. In 1917, World War I threatened to set the movement back once again, but women continued to fight. This time, they successfully argued that the help and actions of women during wartime illustrated their active, equal and deserving role in the country, and in the democratic process.