tu b'av — the fifteenth of av.
The "word" tu is in fact the letters tet and vav which are the Hebrew letters for 15 (tet = 9, vav = 6 | tet+vav=15).
Tu B'Av is the 15th day of the month of Av, a minor holiday in the Jewish Calendar following on the end of the "The Three Weeks," a period of mourning which began with Tzom Tammuz (The 17th of Tammuz) and concluded with Tisha B'Av (the 9th of Av.) It is perhaps because of this that the Tachanun (penitential prayers) are removed from the daily prayer on Tu B'Av [usually recited during the Shacharit (morning) service each day] and it is a practice not to give eulogies at funerals on Tu B'Av. Both traditions suggest the end to the mourning period.
The weeks that follow look forward to the days of preparation and repentance of Elul and Tishrei, ending with Yom Kippur. Liturgically the weekly haftarot readings (prophetical readings) change theme, moving from admonition to seven weeks of consolation before Rosh Hashanah.
The Fifteenth of Av — a joyous day in the Hebrew Calendar.
The Fifteenth of Av is celebrated as a joyous day in the Hebrew Calendar. Several reasons for the celebration of Tu B'Av are given in the Talmud. The earliest mention of the day is in the Mishnah (c. 220 CE) where Rabban Shimon ben Gamaliel is quoted as saying, "There is no better days for the people of Jerusalem than the Fifteenth of Av and Yom Kippur, since on these days the daughters of Israel go out dressed in white and dance in the vineyards" (Ta'anit 4.8).
The holiday which originates in the Second Temple period marks the beginning of the grape harvest, which ended at Yom Kippur. However, Talmudic sources relate the joyous festivities around Tu B'Av and Yom Kippur to more spiritual events. According to them Sages the joy of Yom Kippur is related to the forgiveness of Israel for the sin of the Golden Calf and the joy of Tu B'Av is related to forgiveness for the Sin of the Spies.
Tu B'Av and Rabbinic associations
Talmudic sources gives several reasons for the holiday celebration of Tu B'Av.
Ban on tribal intermarriage by orphan daughters imposed in the Desert lifted
A ban on tribal intermarriage by the orphan daughters without brothers, imposed while Israel was in the desert for forty years, was lifted on the Fifteenth of Av. The ban was the result of the decision regarding the claim for equality in inheritance rights by the daughters of Tzelafchad. Moses' decision was is favor of the daughters but carried the proviso that the daughters must marry only within their own tribe (Num. 27:1-11; 36:6).
Tribe of Benjamin permitted to reenter the community—ban on intermarriage lifted
The re-admittance of the Tribe of Benjamin to the community. The tribe was allowed to intermarry with other tribes after the incident of the concubine of Gibeah (Judg. 19-21).
Deaths of the generation of the spies ceased
The deaths of the generation that came out of Egypt (because of the Sin of the Spies) came to an end in the fortieth year of wandering in the wilderness. The Talmud tells that for forty years the Jews made graves for themselves every Tish B'Av night and slept in them—each year a portion of them died. In the fortieth year those who remained (15,000) woke up next morning surprised to be alive. Thinking they were mistaken in the date they slept in their graves every night until Tu B'Av—the night of the full moon confirming there was no mistake in their calculation of the correct date. When they realized that no more of their generation would die there was great rejoicing.
Healing of the breach between the Northern Tribes and Judah
The removal of the restrictions imposed upon the people of the Northern Kingdom by King Jeroboam which prohibited them from making pilgrimage to Jerusalem. King Hosea ben Elah in an effort to heal the breach between the 10 tribes in the north and the Kingdom of Judah had all the guards removed from the roads leading to Jerusalem. Tradition associates this event with the Fifteenth of Av (Ta'anit 30b).
The miracles of Beitar
The Romans allowed the burial of those who fell at Beitar (during the Bar Kochba revolt, 135 CE). This was designated a double miracle, first the Romans finally gave permission for the bodies to be buried and secpndly because the bodies of the dead were miraculously not yet decomposed despite being exposed to the elements for over a year. The permission for burial was granted on the Fifteenth of Av. This double miracle was the catalyst for the inclusion of the fourth blessing (HaTov VehaMeitiv) of the Birkat Hamazon (Grace after Meals) which added "He who is good and does good." "He who is good," because the bodies had not decomposed; "and does good" because permission was granted.
Wood cutting for the Temple completed for the year
The cutting of the wood for the Temple altar was completed for the year on Tu B'Av. Wood needed to be collected before the rainy season set in to ensure a plentiful supply of sound dry wood was stored until next the summer arrived.
"R. Eliezer the elder says: From the fifteenth of Av onwards the strength of the sun grows less and they no longer felled trees for the altar, because they would not dry [sufficiently]. R. Menashya said: And they called it the Day of the Breaking of the Axe" (Ta'anit 31a).
Increased opportunities for Torah study
Nights were lengthened (after the summer solstice) permitting longer periods of Torah Study. The Kitzur Shuchan Aruch (71:1) and The Rema (Moses Isserles, Yoreh Deah 246:23) note that from the beginning of the Fifteenth of Av one should increase one's hours of Torah study since the nights are growing longer for "the night was created for Torah study."
"From this day onwards, he who increases [his knowledge through study] will have his life prolonged, but he who does not increase [his knowledge] will have his life taken away" (Ta'anit 31a; Bava Batra 121b).
End of planting period
Tu B'Av marks the end of the period of planting trees and crops for the year. Trees planted after Tu B'Av are considered to be planted in the following year (i.e., on Rosh Hashanah) for the purposes of calculating the Sabbatical year.
Marriage and Romance at Tu B'Av
The association between the young women of Jerusalem dancing in the vineyards (Mishnah, Ta'anit 4.8) on the Fifteenth of Av, and ancient fertility rites which are linked the full moon (i.e. 15th day of the month) helps to explain both the ancient and modern popular association of Tu B'Av with romance, love and marriage. This link is played out in religious traditions on this date (e.g., the daughters of Tzelafchad; the intermarriage ban with the Tribe of Benjamin) and in both secular and religious preferences which make Tu B'Av a popular time for Jewish betrothals and weddings. Popular secular celebrations include music dance festivals.