See Devarim (21:12), where it states צפרניה את ועשתה, and this means to fix the nails.
The Ahavas Yisrael of Viznitz zy'a was once in a town for Shabbos, and everyone was surprised when, throughout the Shabbos, he bestowed a lot of honor on a very simple person, who was like "a nobody" in this city.
The Ahavas Yisrael explained, "The Beis HaMikdash was destroyed because of sinas chinam. This means that the Beis HaMikdash will be rebuilt when there is ahavas chinam, love for no reason. This is the reason I chose to love and to honor this simple person. Anyway, he deserves this honor because he is a descendant of Avraham, Yitzchak, and Yaakov." (Heard from the Chernobyler Rebbe Shlita).
People call the month of Av Menachem Av. The Chasam Sofer (Masei) quotes the Yerushalmi that these are actually two months: Av and Menachem. Until Tisha b'Av, it is Av, after Tisha b'Av, it is Menachem. Several times, in the Chasam Sofer's teshuvos, he refers to Av as "the month Menachem".
It states (Yeshayah 66:23) בחדשו חודש מדי והיה, which implies that there's a month that begins in the middle of the month. The Chasam Sofer says that this refers to Menachem, which begins in the middle of Av. The pasuk continues, בשבתו שבת ומידי, this refers to Shabbos Nachamu. The pasuk concludes, 'ה אמר לפני להשתחוות בשר כל יבוא. The Chasam Sofer explains, we will be redeemed from galus at this time of year, and we will bow down before Hashem, in the Beis HaMikdash.
