For the purposes of this discussion, we will be using the tripartite classification of feminist waves devised by Maggie Humm and Rebecca Walker, two notable feminist theorists.
The first wave of feminism took place in the nineteenth and early twentieth centuries. The focus of feminists at this time was on the equalization of legal and political rights, which were hopelessly skewed in favor of men.
During the first wave of feminism, women's rights activists campaigned vigorously in favor of the right to vote, which was finally granted in the United States under the Nineteenth Amendment to the Constitution in 1920 and in Great Britain by the Qualification of Women Act of 1918.
The second wave of feminism lasted from roughly the early 1960s to the late 1990s. Feminists during this period sought to build on the achievements of the first wave; here we can see how the second wave was connected to the previous one, how it represented a continuation rather than a radical break with the past.
If the first wave was primarily concerned with equal rights for women, the second wave was primarily devoted to social and cultural inequalities, which feminist activists like Carol Hanisch argued were inextricably linked to the political inequalities attacked by feminists of the first wave.
Second-wave feminists were at the forefront of campaigns for abortion and contraception rights, seeing them as essential to women being able to exercise control over their own bodies. To a considerable extent, the legalizing of abortion in the landmark Supreme Court case of Roe v. Wade (1973) represented the high-water mark of second-wave feminism.
Similar concerns are shared by third-wave feminism, which has been with us since around the late 1980s. Unlike the second wave of feminism, however, the third wave represents a radical break from its predecessor.
Feminists of the third wave have been highly critical of certain aspects of the second wave, seeing it as being primarily concerned with the lived experiences of upper-class white women. They've also challenged what they see as an essentialist conception of womanhood that excludes a broad range of female experiences, in particular those of women of color.