Tu B'Av literally means "the fifteenth of Av." While it isn't exactly a holiday, it is singled out as a special date on the Hebrew calendar by the Mishnah:
(ח) אָמַר רַבָּן שִׁמְעוֹן בֶּן גַּמְלִיאֵל, לֹא הָיוּ יָמִים טוֹבִים לְיִשְׂרָאֵל כַּחֲמִשָּׁה עָשָׂר בְּאָב וּכְיוֹם הַכִּפּוּרִים, שֶׁבָּהֶן בְּנוֹת יְרוּשָׁלַיִם יוֹצְאוֹת בִּכְלֵי לָבָן שְׁאוּלִין, שֶׁלֹּא לְבַיֵּשׁ אֶת מִי שֶׁאֵין לוֹ...וּבְנוֹת יְרוּשָׁלַיִם יוֹצְאוֹת וְחוֹלוֹת בַּכְּרָמִים. וּמֶה הָיוּ אוֹמְרוֹת, בָּחוּר, שָׂא נָא עֵינֶיךָ וּרְאֵה, מָה אַתָּה בוֹרֵר לָךְ. אַל תִּתֵּן עֵינֶיךָ בַנּוֹי, תֵּן עֵינֶיךָ בַמִּשְׁפָּחָה. שֶׁקֶר הַחֵן וְהֶבֶל הַיֹּפִי, אִשָּׁה יִרְאַת יהוה הִיא תִתְהַלָּל (משלי לא). וְאוֹמֵר, תְּנוּ לָהּ מִפְּרִי יָדֶיהָ, וִיהַלְלוּהָ בַשְּׁעָרִים מַעֲשֶׂיהָ...
Rabbi Shimon ben Gamaliel said: There were no days of joy in Israel greater than the fifteenth of Av and Yom Kippur. On these days the daughters of Jerusalem would go out in borrowed white garments in order not to shame any one who had none...The daughters of Jerusalem come out and dance in the vineyards. What would they say? Young man, lift up your eyes and see what you choose for yourself. Do not set your eyes on beauty but set your eyes on the family. “Grace is deceitful, and beauty is vain, but a woman that fears the Lord, she shall be praised” (Proverbs 31:30). And it further says, “Give her of the fruit of her hands; and let her works praise her in the gates” (ibid, 31:31)...
The Mishnah describes a kind of "meet market," in the most innocent sense: Women, all dressed alike in borrowed clothing, would go out into the vineyards and invite the men to connect with a potential spouse. Their words encouraged the men to look beyond the physical characteristics of those they encountered and to focus instead on a woman's character.
The Talmud, in trying to understand this Mishnah, connects this date with the famous story of the daughters of Zelophehad in the book of Bamidbar. When Zelophehad dies, leaving behind only daughters, these women realize that the laws of inheritance mean that their father's land will be lost to his tribe. They come to Moses with their request to keep their father's land, and God intervenes and decrees that the daughters will inherit the land, but they must marry within the tribe so that the land stays among their father's people. According to the Talmud, this rule was temporary, and later on in Jewish history, women were allowed to marry from any tribe they chose. Tu B'Av, in this understanding, is the celebration of women who have more men from whom to choose!
ט"ו באב מאי היא אמר רב יהודה אמר שמואל יום שהותרו שבטים לבוא זה בזה מאי דרוש (במדבר לו, ו) זה הדבר אשר צוה ה' לבנות צלפחד וגו' דבר זה לא יהא נוהג אלא בדור זה
What is the special joy of the fifteenth of Av? Rav Yehuda said that Shmuel said: This was the day on which the members of different tribes were permitted to enter one another’s tribe, by intermarriage. It was initially prohibited to intermarry between tribes, so as to keep each plot of land within the portion of the tribe that originally inherited it. This halakha was instituted by the Torah in the wake of a complaint by the relatives of the daughters of Zelophehad, who were worried that if these women married men from other tribes, the inheritance of Zelophehad would be lost from his tribe (see Numbers 36:1–12). What did they expound, in support of their conclusion that this halakha was no longer in effect? The verse states: “This is the matter that the Lord has commanded concerning the daughters of Zelophehad, saying: Let them marry whom they think best; only into the family of the tribe of their father shall they marry” (Numbers 36:5). They derived from the verse that this matter shall be practiced only in this generation, when Eretz Yisrael was divided among the tribes, but afterward members of different tribes were permitted to marry. On the day this barrier separating the tribes was removed, the Sages established a permanent day of rejoicing.
The Talmud also describes six other happy events that are commemorated by Tu B'Av. Finding a unifying theme can be tricky, but we encourage you to check out the full story here! One of the common threads, however, is a sense of repairing that which was broken over the course of the events leading to Tisha B'Av, the day of mourning that comes just a few days before Tu B'Av. For example:
(אמר) רבה בר בר חנה א"ר יוחנן יום שכלו בו מתי מדבר דאמר מר עד שלא כלו מתי מדבר לא היה דבור עם משה שנאמר (דברים ב, טז) ויהי כאשר תמו כל אנשי המלחמה למות וידבר ה' אלי אלי היה הדבור
Rabba bar bar Ḥana said that Rabbi Yoḥanan said: The fifteenth of Av was the day on which the deaths of the Jews in the wilderness ceased. The entire generation that had left Egypt had passed away, as the Master said: After the sin of the spies, on account of which the Jews of that generation were sentenced to die in the wilderness, as long as the death of the Jews in the wilderness had not ceased, God’s speech did not come to Moses, as it is stated: “And it came to pass, when all the men of war were consumed and dead from among the people, that the Lord spoke to me, saying” (Deuteronomy 2:16–17). This indicates that only then, after the last member of that generation had died, was God’s speech delivered to me, i.e., Moses, but not beforehand. When the Jews realized that the decree that God would not speak to Moses had been lifted, they established that day as a permanent day of rejoicing.
The 9th of Av is the day when God decreed that all the Israelites who left Egypt and were therefore implicated in the sin of the spies, would die in the desert and therefore would not reach the land of Israel. In contrast, the 15th of Av is the day when the deaths stopped. Not only that, the Talmud tells us that once the punishment was over, God once again began to speak with Moses. If Tisha B'Av is emblematic of the breaking down of the relationship between the Divine and the nation, Tu B'Av is a time of rekindling flames and building new relationships.
Likutei Halakhot, a Hasidic work from the 19th century, makes this connection clear:
כִּי ט"וּ בְּאָב הוּא בְּחִינַת הַתִּקּוּן וְהַהַמְתָּקָה שֶׁל תִּשְׁעָה בְּאָב...
...therefore the fifteenth of Av is in the nature of a sweetening and a repair of the ninth of Av...
On the 9th of Av, we recommit ourselves to the process of improving all that is broken in our world, and on Tu B'Av, we celebrate all the possibilities that we might create. While on Tisha B'Av, we focus on the forces of destruction throughout Jewish history, on Tu B'Av, we engage in the "tikun," or act of fixing, of releasing as much love as possible into the world.