A summary of some moments in feminist history and "waves"
The terms 1st, 2nd and 3rd waves were created by feminists who thought the feminist movement of the 1960 and 70s left out large portions of the female population, specifically, all of those who weren't white and upper or middle class and straight.
Though critique of this privilege given to (mostly) suburban white female issues began earlier, by the 1990s, with a variety of input from women of color, homosexual and trans women, women in 3rd world nations, and even punk Riot Grrrls with zines - some women thought the focus of feminism was too small - not inclusive enough.
1st wave feminism: voting rights, property rights, birth control (that existed at the time - condoms or sponges and, just as important, education about sexuality and how to prevent conception.)
2nd wave feminism: sexual freedom, legislative work to change sexist law, integration into the workplace, equal funding, integration into the political arena
3rd wave feminism: sexual freedom, inclusion of gendered females, diversity, inclusion of women of color and women from other cultures - plus the issues surrounding both 1st and 2nd wave feminism.
1st wave feminism is generally thought of in terms of the Suffrage Movement (gaining the right to vote.) That places it within the 19th and 20th century.
However, even before this, women, such as Mary Wollstonecraft (mother of the woman who wrote Frankenstein, fwiw), who came of age during the revolutionary period in America and France, wanted the ideas of the Enlightenment extended to females in society. Back then, a female could not obtain an education beyond things that she could use to run a household, for the most part.
There were exceptions, such as Ida Lovelace (after Wollstonecraft), but the rule was that females were purposely kept ignorant - in the same way that slaves were purposely kept uneducated. She wrote A Vindication of the Rights of Woman, that talked about the sexism (that did not have a name at that time) that controlled the way in which society functioned, just as monarchy and the church controlled all of European society.
Wollstonecraft was British, but she is one of the most influential "mothers" of western feminism because of her writings that recognized women had no place to go in society, except under the control of a male. She argued that women were capable of receiving an education without becoming immoral and that society benefited by educating women as well as men. She ran a school, helped a friend escape from an abusive husband, helped an American lover smuggle stolen goods from French aristocrats to finance the French Revolution, traveled alone with her illegitimate child and wrote about it, viewed and wrote about The Terror first hand, and was a friend of leading intellectuals of the day in GB and the newly founded U.S. - like John Adams, Joseph Priestly, and the founder of anarchism, William Godwin.
There were a lot of parallels between the position of women and slaves - though, of course, the color of a white woman's skin still gave her more options, even tho narrow, than a black man or woman in America. Nevertheless, because of religion, for the most part, women were forced to remain second-class citizens for longer than black men - who gained the right to vote before any woman.
Suffragettes were attacked in the streets for demanding the right to vote. By men. They were vilified by politicians and preachers - just as any social change is attacked today. With the 1920s, women were divided on issues like prohibition, but, in order to exist in "polite society" women could either be "good" or "whores" - i.e. go to speakeasies or sit home. This same sort of division existed long before this time - it's a division put in place by religious views. Even the suffragettes failed to account for their own privilege. They tried to exclude women of color, like Ida B. Wells.
(Imo, btw, religion has been one of the chief causes of oppression for women across societies and time. you see it now. you saw it then. you saw it when some asshole was blaming women for opening Pandora's Box or offering Adam an apple. Wollstonecraft, back in the day, recognized this and said that, as a culture we need to get away from the "myths of Prometheus" and move to rational thought.
Anyway, then, in 1949, Simone de Beauvoir, a French writer/philosopher, wrote a book called The Second Sex. In that book, she talked about the way in which men viewed women as "objects" rather than "subjects." Women are treated as "creatures" whose lives were not worth examining beyond their roles in relation to men. They were "exoticized" - in the same way that racism works - or, the way that religions dehumanize "the other." (As she had seen with The Holocaust, and as has been done to women in regard to religion for a long time.)
That inhumanity has been extended to women throughout history. Women are considered abnormal because they're not male. Their lives were not as valuable - Their experiences not as important - Their perspective not worth consideration - This, again, is just how racism has played out in American society, as well.
The Second Sex is regarded as the beginning of 2nd wave feminism., but the idea, as a movement, did not take hold until the 1960s, with the 1963 publication of Betty Friedan's The Feminine Mystique.
But the foundation for feminism was laid in WWII, when women entered the workplace in massive numbers to make up for the loss of men who were sent to fight. Of course, prior to WWII, a lot of women (and children) worked - in factories, with no protection by law, and some women, like Jane Addams, gave focus to the plight of immigrant women in the U.S.
But after WWII, the U.S. embarked on a massive propaganda campaign to tell middle-class white women to get out of the workforce so that men could have jobs. They did - but many of them realized that it was not enough to have a life that only mattered b/c of a husband or children. They wanted some sort of financial independence and interests that were their own - A life apart from their families, as every other member of the family was allowed to have. White middle class privilege was still at work in this recognition, though, as women of color often worked for outside their homes.
In the 1960s, women gained access to more reliable birth control. The state could no longer enforce religious beliefs about women's outcomes based upon their sexual lives. The reason religions hate birth control is because they continue to maintain the same patriarchal attitudes toward females now as they did when they were aligned with monarchies in the 1700s and before.
Now, to the issue that causes contention, often, here:
In the 1970s and 1980s, one group of feminists began a focus on pornography. Other feminists at the time, and now, disagreed with the positions of the anti-porn faction because they viewed porn as a free speech issue as well as an issue of women's objectification. The anti-porn faction developed a line of action that worked to suppress porn as a violation of a woman's civil rights.
One of the most vocal women in the anti-porn movement was Andrea Dworkin. She also wrote about right wing women who work to undermine all women - conservative women. We still see them at work today - in the Republican Party. But she also made claims about pornography that said it promoted rape and child abuse. She wrote a book that claimed all heterosexual intercourse degrades women.
She crossed a line with many people with that pov. She claimed she was misunderstood and that, eventually, people would be able to have sex that was not coercive. But for now...
Other feminists responded that they could define their sexuality themselves - and could enjoy porn - whether those women were homo or hetero-sexual. For some, however, that position would be "false consciousness," i.e. it is impossible to rise above the ideology of sexism and patriarchy in which someone lives.
The "porn wars" on this site stem from the clash of these two povs.
Anyway, back in the 1960s, Democrats, under Kennedy, took up the cause of women's rights and women began their long-time association with the Democratic Party at the same time that African-Americans moved from the party of Lincoln (that was becoming the party of racists and Reagan and religious right wingers) to the party that passed the civil rights act.
In the 1960s and 70s - there were a lot of different people in American society who wanted change - Native Americans, African-Americans, women, homosexuals... and immigrants, esp. Latinos...working people in general became the focus of attack after Democrats lost many states due to their alignment with women and people of color.
And those battles for change are the ones that are still being fought today.
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There's so much more to this whole history - but this is a selected short version. 
