This was the first animated movie that made me cry as an adult.  
It still does.

Two children are left as orphans in World War 2 and have to survive.  Such a basic premise, but this shows intimately what the effects of war are on children (a topic not covered by other movies).  And as it's about children, it has more of an emotional impact.  
Described as one of the greatest war movies of all time by Roger Ebert, the work of art will impact you like no other anime. 

Its interesting to note that this was released originally with My Neighbour Totoro.  Both are films about childhood.  But where Totoro is about innocence maintained and the joy of childhood, **Fireflies is innocence lost**, a light dimmed after a short period.