1. The fifteenth of Av is a happy day, because of a number of happy things which happened on that day through the generations, as will be explained. Because of this we may not fast on this day, nor may we say Tachanun. (Levush 580)
2. These are the things which happened on this day: 1) After the sin of the spies it was decreed that our fathers would die in the desert and not enter the Land of Yisrael. On each day on the ninth of Av fifteen thousand four hundred and eighty-nine people would die. In the last year no one died, and they thought that they had been mistaken about the date, until the fifteenth arrived and they saw the full moon and realized that the ninth of Av had definitely passed, and that Hashem had forgiven them for that sin. They made the day into a festival. 2) The tribes were allowed to intermarry, as in the beginning they thought that any woman who inherits land may only marry someone from her own tribe, whereas there came a time when they realized that this law had only been said regarding the first generation who came into the holy land, but the following generations could allow such a woman to marry into any tribe. This took place on the fifteenth of Av, and they were happy about this and made it a festival.
