On Yom Kippur, G-d forgave the Children of Israel the transgression of the golden calf. It was the day that the second tablets of stone were given to the Jewish people as a replacement of the first ones that had been broken. As a result of this, Yom Kippur became the day of Teshubah (repentance) and atonement, for all time.
The 15th of Ab was also a day of forgiveness. It was the day when Benei Yisrael (the Children of Israel) received forgiveness over the sin of the spies. That is why the early generations considered the 15th of Ab to be on a par with Yom Kippur.
The reason why it was deemed acceptable, indeed virtuous, for the daughters of Israel to go out and dance in the vineyards is because, since these days were ones of purification and holiness, there was no concern about any lack modesty or of inappropriate behavior. Even the dancing was entirely Leshem Shamayim (for the sake of Heaven).
(See Sefer HaToda'ah)
15th of Ab, Tu B'av