There are two answers that take basically the contemporaneous Trotskian view. It is useful but is roughly the equivalent of asking of reading Jefferson Davis's Rise and Fall of the Confederate Government and claiming a complete knowledge of the American Civil War. The sources are tainted by their political leanings, though obviously a necessary part of the complete whole.
Russia is often portrayed as exceedingly patriarchal. This is because Russia has been traditionally seen as backwards and patriarchy is often (unjustly) associated with backwardness. (Seriously, I could write a whole post on how the idea that feminism is something that only exists in the 'enlightened and civilized' west has direct colonialist/imperialist roots.) The reality is that improving the place of Russia women had been a state goal since the late 17th and early 18th century. Women gained the right to inheritance in 1714. While the specific law was repealed in 1730, it had already created a class of female landowners. A new version was promulgated next year and women continued to inherit and hold land in Russia in higher numbers than western Europe right up to the Revolution. The Tsarina (who was regnant) established a women's college in 1765. And so on. Feminism became a huge force in the second half of 19th century Russia. By 1900, Russia had more female professionals than any other country. Late 19th century travelers often commented on the freedom of women.
On top of that, the mass mobilization of World War 1 had strengthened feminism even further as women entered the workforce. This was a less painful transition for Russia than the other powers since Russia already had relatively high rates of female workforce participation. There was little opposition to granting women the vote after the February Revolution. The Revolutionaries, who were not socialists, wrote language that guaranteed them the right to hold any political office. This makes Russia the first major power to have granted universal female suffrage.
So the idea that Socialism or the Soviet Union's revolution was the main driver behind women's rights is propaganda in line with claiming the Chinese Communists drove out the Japanese. It's not a complete fabrication but it ignores other huge forces that contributed, including explicit anti-Communists. When Trotsky claimed that the Soviet government had done 'incomparably more than any other government' to improve the lot of women, he wasn't wrong. But not only could the Provisional Government make the same claim, so could the Tsar! For example, looking at the experience of women soldiers: the Tsarist regime made more extensive use of women at the front than the other western powers. They even had a small number of frontline female troops and female NCOs. The Provisional Government then opened up the military and created female combat troops and officers. The Soviets pushed these policies further and managed to make the military about 2% female by 1920.
The February Revolution's goals included extending the rights of women as well. The Communist program could only increase these grants. Here's the a list of several programs of the Communist government. Where there is an asterisk, the Communists were simply continuing or enacting more extreme versions of reforms that had been started by the previous, non-Communist revolution.
1.) The involvement of a Church in marriage was forbidden.*
2.) It became easier to change the family surname.
3.) Illegitimate children were no longer subject to any bastardy laws.
4.) Increased maternal leave and work rights.*
5.) Increased material benefits like childcare and state support.*
6.) Used their new control of the economy to even more strongly encourage women into the workforce.*
7.) Abortion was legalized in more cases. This was controversial enough it took til 1920.*
8.) Various minor laws that were often more symbolic than practical. They briefly banned headscarves, for example, only to repeal the ban but not use them in uniforms anymore.
Several things the Communists could not extend any further. For example, the February Revolution abolished laws against sexual immorality so thoroughly they basically no longer existed. But the Soviets also did some things (like increased minimum wage) disproportionately benefitted women. Interestingly, the Communists actually rolled back alimony and child support, seeing them as patriarchal and capitalist holdovers. They also established the Zhenotdel, basically a ministry meant to advance the cause of women. However, unlike women's ministries in the west, the Zhenotdel was meant to create the 'New Soviet Woman' (a counterpart to the New Soviet Man). They emphasized duty, Communist orthodoxy, and obedience to the state rather than individualist empowerment.
The divorce rate skyrocketed. It was so high that it created problems on the front, with absent soldiers being divorced by the women they left behind. These stories were lurid and played on male fears. Yet it's true that it was possible for a woman to divorce her husband on the front and gain possession of their home and possessions. Interestingly, the Chinese Communists had the same issue during their civil war and eventually banned divorcing a soldier at war. The Russians didn't but they did make divorce slightly more difficult and wrote new laws on the division of marital property. The number of women in the workforce doubled several times, driven both by positive incentives and Soviet persecution of homemakers.
1928 saw a shift towards Stalinism. This entailed the end of the New Economic Program, the persecution of a wide variety of groups, the suppression of alternative power centers, and bloody purges. Stalin declared explicit class warfare against enemies of the Revolution and he meant it. Women and feminism were not a primary target of any of this and were arrested, executed, and exiled in much smaller numbers than their male counterparts. Nevertheless, the Zhenotdel was disbanded in 1930. Throughout the decade, abortion was made illegal again, divorce was made much more difficult, and bastardy was reintroduced. Women continued to be encouraged to work but the New Soviet Woman now included domesticity and childbearing. They were still declared to be equal to men though.
Some feminists organizations were suppressed. Again, I want to emphasize that women were a minor part of the victims. There were less than 110,000 women in the gulags in 1940. There were 1.2-1.5 million men in the system at the same time. The proportion of executions was similar. Additionally, the state continued to tolerate many women's groups. For example, the Soviet government suppressed a mostly male organization dedicated to the study and preservation of Azeri culture but allowed an organization for the advancement and study of Azeri women. This tolerance was notable at a time when the Soviet state literally engaged in the suppression of chess clubs. But it reveals part of the pattern: women's organizations were allowed to continue to exist where they were set against something the Soviet state disliked. In this case, traditional Azeri culture was patriarchal, the Soviet Union did not like traditional Azeri culture, and so it encouraged an organization meant to fight patriarchy.
More of course can be said, but this older answer of mine does look narrowly at natalist policy and reproductive Rights in the period so may be of interest to you.