Unlike the hatoros throughout the year which relate to the weekly parsha, the haftoros known as sheva d'nechemta reflect the character of this time of the year. The Gemara (Megillah 4a) explains, "Moshe tikein lohem l'Yisroel sheyehu sholaim v'dorshin b'inyano shel yom - Moshe enacted the practice of inquiring and elaborating on the theme of the day." The fact that the gemara applies this principle to Purim demonstrates that this institution is not limited to the yomim tovim, but extends to other significant periods of the year. Rav Soloveitchik suggests that it was this takonas Moshe which guided our sages to institute this special series of haftoros.
Although all seven of the haftoros are taken from sefer Yeshayahu, surprisingly their order does not follow the sequence of the navi. The haftorah of Parshas Shoftim for example, is found in perek 51, whereas the haftorah of Parshas Re'eh which is read a week earlier is taken from perek 54.
Tosafos (Megillah 31b s.v. Rosh Chodesh) explains "d'derech hanechamos l'hiyos holchos u'm'shubachos yoser" - the order of these haftoros reflect the unique progression of the quality of consolation. The Pesikta Rabbasi explains that although the first of the sheva d'nechemta assures Bnei Yisroel of true consolation, "nachamu nachamu ami - comfort, comfort, my people", it is not Hashem who consoles Bnei Yisroel directly, but rather the navi as an emissary of Hashem who promises consolation.
Then next hatorah which begins "vatomar Tzion azovani Hashem, v'Hashem shecheichani - and Tzion said Hashem has forsaken me, Hashem has forgotten me", underscores the refusal of Tzion to accept an indirect nechama. We yearn for Hakadosh Baruch Hu to console us directly. The haftorah of Parshas Re'eh reiterates this feeling of abandonment and despair - "aniyah so-ara lo nuchama - afflicted storm tossed, unconsoled one."
Ultimately, Hashem Himself consoles us. Hence the haftorah of Parshas Shoftim begins, "Anochi Anochi hu menachemchem - it is I, I am He who comforts you."
One of the many lessons of this medrash is the need for an avel to accept divrei nechama. Indeed, Rav Chaim Soloveitchik once wrote, "yavo'u divrei tanchumin ka'asher kein hu hamitzvah l'kabeil tanchumim - may words of consolation come, as it is a mitzvah to accept words of consolation", emphasizing the mitzvah incumbent upon the avel to accept the birchas aveilim.
In these extremely difficult and trying times, we yearn for the fulfillment of the majestic prophecy, "Anochi Anochi hu menachemchem."