Ah, Helen! This is a great sentence! "Died back" in this case means that the leaves have fallen or the growth has stopped--but not completely dead. You know how Spring causes new growth yet sometimes things stop growing in Autumn (Fall), foliage can "die back."
Incidentally, we will also use "cut back" on bushes/shrubs/trees when we are snipping away at limbs and leaves that cause the bush to look messy. Sometimes the bush gets too full, so we will "cut back."
Ex: Yesterday I cut back my bushes in preparation for the wedding.