Our mourning and our tears build the Beis HaMikdash. The Shlah HaKadosh (Masechta Taanis, Ner Mitzvah, #33) writes that we don't mourn on Shabbos because it is forbidden to build on Shabbos, and mourning builds the Beis HaMikdash!
Hashem is building the Third Beis HaMikdash in heaven. The construction materials are our tears and mourning, which Hakadosh Baruch Hu takes and builds with them the third Beis HaMikdash in heaven, brick by brick, stone by stone. When it is completed, it will come down from heaven. Therefore, it states (Tehillim 147), 'ה ירושלים בונה, "Hashem builds Yerushalayim." It is written in the present tense. The Chasam Sofer zy'a (Drush 7th Av, 5599) asks that it seems that the pasuk should state in the future tense יבנה 'ה ירושלים, "Hashem will build Yerushalayim." But the answer is that Hashem is building the Beis HaMikdash now, as Chazal tell us, the third Beis HaMikdash will come down from heaven fully built (see Rashi on Rosh Hashanah 30. צ"ל ה"ד). It is being built by Hashem and will come down when completed. The construction material is our mourning and our tears.
The Gemara (Makos 24) says: Rabban Gamliel, Reb Elazer ben Azaryah, Reb Yehoshua, and Reb Akiva traveled to Yerushalayim. When they came to Har HaBayis, they saw foxes coming out of the Kodesh Kodoshim. Rabban Gamliel, Reb Elazer ben Azaryah, and Reb Yehoshua cried. Reb Akiva laughed. They asked Reb Akiva, "Why are you laughing?" He asked, "Why are you crying?" They said, "The place about which is states יומת הקרב והזר (that only kohanim may go there and anyone else will die) has foxes prancing about it. Shouldn't we cry?" Reb Akiva replied, מצחק אני לכך, "That is precisely why I'm laughing." Reb Akiva explained to them that after he saw the actualization of the prophecies of the destruction, he felt reassured that the prophecies of redemption would transpire. From Reb Akiva's words, מצחק אני לכך it seems that he was laughing because they were mourning.
Rebbe Yisrael of Tchortkov zt'l explains that he was happy that Yidden were mourning over the Churban because those tears will build the third Beis HaMikdash. As the Zohar (vol.2 p.12:) tells us, "The redemption of Bnei Yisrael depends solely on crying."
Benefits Earned from the Mourning
Many benefits come from mourning. Reb Chaim Palagi (Moed l'Kol Chay, Av, #61) writes, "When one mourns for the Churban Beis HaMikdash, his sins are forgiven, he will live a long life, his children won't die in his lifetime, and his children will live long."
Rebbe Pinchas Koritzer zt'l (Imrei Pinchas 404) says, "Tisha b'Av atones for sin because people are very broken. This is why after Tisha b'Av, we feel slightly similar to how we feel after Yom Kippur."
Reb Elyah Lopian zt'l said that in Kelm, they emphasized the word כל in the phrase בשמחתה ורואה זוכה ירושלים על המתאבל כל, "Everyone who mourns for Yerushalayim merits seeing its joy..." כל, everyone, means even those who committed severe aveiros. They, too, will merit to experience the happy days when Moshiach comes. This is because mourning sanctifies and purifies and cleanses from aveiros. Therefore, המתאבל כל, everyone who mourns, even the sinners, will merit to experience the joy of the geulah (Beis Kelm, p.396).
The Chasam Sofer zt'l said that those who cry for the Churban merit good children. (Therefore, as one mourns, it is an auspicious time to daven for your children's success in Torah and yiras Shamayim.)
The Kav HaYashar (ch.93) writes, "I received a true kabbalah: Whoever is always distressed about the galus HaShechinah, he will merit the crown of Torah."
Reb Yehudah of Asad zt'l would save the tears that fell from his eyes at Tikun Chatzos and give them to bachurim at risk of being drafted into the army. This segulah helped them (Toldos Shmuel, as told by the testimonies of Reb Yosef Tzvi Dushinsky zt'l and others).
Tana d'Bei Eliyahu (Rabba 20 אחת פעם ה"ד) tells that the nations פרס and מדי were created and came to the world as a reward for Koresh, because he cried and mourned when the goyim destroyed the Beis HaMikdash. The Chofetz Chaim’s zt'l made a calculation and found that Koresh was seven years old at the time of the Churban. A child of seven doesn't fully understand the devastation of the Churban. Nevertheless, he cried, and he was rewarded for his tears. How great will be the reward for the Yidden who mourn and weep for Yerushalayim!
Psikta d'Rav Kahana (ch.25) writes that Hashem swears, "Whoever waits for My kingdom [which will be revealed when Moshiach comes] I will testify for him for his benefit."
Shulchan Aruch (Orach Chaim 554:25) states, וכל בשמחתה ורואה זוכה ירושלים על המתאבל, "Whoever mourns for Yerushalayim merits seeing its joy." The Meforshim (Sfas Emes, Kedushas Levi, and others) explain that ורואה זוכה, "merits and sees," is written in the present tense. This is one of the segulos of mourning. When one mourns for Yerushalayim, he immediately experiences and feels in his heart the joy of the redemption.
At a chasunah, we say the brachah of שוש תשיש, which is a tefillah for the rebuilding of Yerushalayim. The Sfas Emes zt'l explains that we want the joy of the chasunah to be complete. We do this when we mourn for Yerushalayim. The mourning draws down to us a scent of the future joy of Yerushalayim. This completes the joy of the chasunah.
Rebbe Pinchas of Koritz zt'l (Imrei Pinchas 380-381) writes, "On Tisha b'Av, when we sit on the floor and daven, we can accomplish...