The Shulhan Aruch (Orah Haim 284) writes that after the Torah reading on Shabbat the congregation reads a selection from the Nebi’im (Prophets) related to the content of the Torah reading, which we commonly call the Haftara. The Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) explains that the practice of the Haftara reading was enacted during the time of Antiochus’ rule over Eretz Yisrael, in the time of the Hashmonaim, when the Jews were not allowed to conduct the public Torah reading. The Haftara reading was instituted so that the people would remember the Torah reading through the reading of a portion from the Nebi’im that relates to the content of the weekly Parasha. This became a beloved practice and was thus continued even after the decrees were no longer in place.
Unfortunately, many people grow weary and impatient by the time the Torah reading ends, and do not pay attention to the Haftara reading. One must ensure to follow the Haftara reading in a Humash, and should certainly not engage in conversation during the reading.
The Berachot recited after the Haftara reading make reference to important subjects such as Malchut Bet David (the Davidic dynasty), our national redemption, the service in the Bet Hamikdash, glorifying the Name of God, and Siduk Ha’din (affirming the justice of God’s judgment), and our Rabbis teach us that these Berachot are equal in importance to the Kaddish. Therefore, mourners within twelve months of the passing of a loved one should try to be given the honor of reading the Haftara, so they can recite the Berachot. Furthermore, according to the Zohar, reading the Haftara is very beneficial for the soul of a deceased family member around the time of the Yahrtzeit, especially the Shabbat before the date of the Yahrtzeit, which is the day when the soul has the opportunity to be elevated. The Berachot recited over the Haftara and the "Amen" responses are very beneficial for the soul on this Shabbat, and therefore one should try to receive the honor of the Haftara reading on the Shabbat before the Yahrtzeit. However, the Kaf Ha’hayim (Rav Yaakob Haim Sofer, Baghdad-Israel, 1870-1939) warns that one should not make an argument in the synagogue in order to receive this honor. One brings far greater benefit to the soul of a loved one by avoiding conflict than he does by instigating a quarrel in the synagogue in order to read the Haftara.
Summary: Congregations are required to conduct the Haftara reading after the Shabbat Torah reading, and every congregant should ensure to remain silent during the Haftara reading and follow along from a Humash. It is very beneficial for the soul of a deceased person for a family member to read the Haftara with the Berachot within twelve months of his passing, and on the Shabbat before the Yahrtzeit, but one should not instigate a quarrel in the synagogue to receive this honor.
