used at the beginning of children's stories to mean "a long time ago"

Once upon a time there was an ugly duckling. 从前，有一只很丑的鸭子。

used when referring to something that happened in the past, especially when showing that you feel sorry that it no longer happens

Once upon a time people knew the difference between right and wrong, but nowadays nobody seems to care. 从前，人们还知道是非曲直，可是如今似乎没人在乎这些了。