Tisha beAw (literally "the ninth of the month Aw") is the second-most important fast day in the Jewish calendar (after Yom Kippur). This is the day that both the first and the second temple were distroyed – a tragedy for the Jewish people at the time.
But as a non-so-orthodox Jew, what does the temple mean to me? I am not really looking forward to it being rebuilt. Aside from the little problem with the building standing at its location at the moment, why would I want a 2000-year-old rite with sacrifices to be reinstated? Even if we could ignore the sacrificing-animals-part (you could argue that not all sacrifices are animals, most of the sacrifices are eaten and slaughtering animals just for food is also cruel), how am I supposed to find meaning in the concept of sacrifices in a temple by priests? In my humble opinion Judaism was lucky that it had to develop alternative ways of worship and was thus able to survive when sacrificial cults went out of fashion.
But then, what do I do with a day of mourning for the temple?
One possibility is, to look for other sad occasions in Jewish history that are connected to this date. The expulsion of Jews from Spain for example. Or, alternatively, view the historical context where the destruction of the temple did not only destry a building, but marked the end of an era of Jewish life in the region with lots of people killed. Which happened several times in Jewish history. And which may happen again.
Alternatively, use the day for fasting and introspection and spiritual renewal without a connection to tragedy. I am not sure how well that can work, but I might try it.