In reading Parshat Zachor,Devarim 25: 17-19, we fulfill the command of remembering the hostility of Amalek; we remember, we do not forget, we erase the memory of Amalek. For some, Rambam for example, the obligation relates to war against this nation. For others, including Rav Soloveitchik, the message is more universal, expressing broader religious messages, not necessarily related to war.
The obligation to read the Torah in the synagogue is rabbinic. The obligation to read Parshat Zachor, however, is min ha'Torah, biblical. As a result of this, women may be obligated, although there are other parshiot through which this mitzvah can be fulfilled. Because women may be obligated, the tradition is to have a reading of Parshat Zachor later in the day, so that all women may attend.
We have assumed that Parshat Zachor or other passages suffice. Sefer Hinuch writes that perhaps once a lifetime is enough, or even once a year. The Hatam Sofer says that once a year suffices, while once in one's life does not.
How should the mitzvah be carried out? Parshat Zachor should be read from a Torah scroll. Some require a minyan, while others do not. Does the principle of shome'ak'oneh, listening to the reading is as if you read the text, apply? Most say that it does apply.
How should the word zekher or zeikher be pronounced? The Mishna Berura says that both should be said. For some it is sufficient to read both without repeating the pasuk, while others require repeating.
Another issue: Some argue that those who read Hebrew with an Ashkenazic pronunciation should hear Parshat Zachor read in that way, whereas those who read Hebrew with a Sephardic pronunciation should hear Parshat Zachor read in that way.
Regarding the hostility of Amalek, antisemitism has a long history. Before Christianity and under Christianity, Jews suffered. Key events include medieval Jewish-Christian disputations, the 1648 Chmielnicki massacre with 100,000 victims, and persecution in Nazi Europe during the 1930s and 1940s, with the death camps claiming 6,000,000 victims. Jews experienced social antisemitism, political antisemitism, and economic antisemitism. There is antisemitism in today's universities. Parshat Zachor is a call to be aware of all forms of antisemitism.
May Hashem grant us the zechut of living in a time of peace.