In Masekhet Ta'anit Rabban Shimon ben Gamliel said that "There were no better days for the People of Israel than the Fifteenth of Ab and Yom haKippurim, since on these days the unmarried girls of Jerusalem would go out dressed in white to dance in the vineyards. They would say to the bachelors: 'Young man, consider who you choose (to be your wife)'." Many young men and women would find their future spouse on this day.
To explain why this day was chosen for such a joyous encounters the Talmud mentions the events that happened on the 15th of Ab throughout Jewish history.
1. As we know from the story of the Tish'a beAb (see this), when the People of Israel protested against going to the land of Israel, every one older than 20 years old was condemned to die in the desert. Forty years later, on the 15th of Ab, this decree was canceled.
2. In order to ensure the orderly division of the Holy Land between the twelve tribes of Israel a few restrictions were established to restrain marriages between members of different tribes. A woman who had inherited land from her father was forbidden to marry out of her tribe, because her children--members of their father's tribe--would cause the transferring of land from one tribe to another tribe by inheriting her estate(Bamidbar, Chapter 36). These restriction were lifted on the 15th of Ab and marriages between different tribes were permitted.
3. The 15th of Ab was also the day on which the tribe of Benjamin, which had been excommunicated for its behavior in the terrible incident of the "Concubine at Givah" (Judges 19-21) was readmitted into the community of Israel.
4. The Romans permitted the burial of Jews killed in the Betar revolt (138 CE). After the Romans had destroyed the Second Holy Temple, the emperor Hadrian planned to transform Jerusalem into a pagan city-state with a shrine to Jupiter on the site of the Bet haMiqdash. This led to the revolt of Bar Kochba, whose guerilla army succeeded in actually throwing the Romans out of Israel and establishing, albeit for a brief period, an independent Jewish state. It required large numbers of Roman troops to crush the revolt. Bar Kokhba made his final stand in the city of Betar, located southwest of Jerusalem. It was estimated that hundreds of thousands of Jews lived in Betar, and they were all massacred "until their blood flowed into the Mediterranean Sea." The Romans did not allow the Jewish bodies to be buried. According to Jewish tradition, the bodies lay in the open but did not rot, until three years later on the 15th of Ab, burial was finally permitted.
Click here to read more about the events that took place on the 15 of Ab