One of the Buddha's most important lessons was that of impermanence. When we can realize that everything is impermanent, we can begin to find freedom from our desires and suffering.
But we can't just say to our pain/suffering, "You are impermanent, so GO AWAY!" We need to acknowledge our suffering or pain to figure out the root cause and also to transform that suffering into healing. Being mindful of impermanence will also help us be more appreciative of our loved ones. We know that we wont be here forever, we know we will probably outlive our pets, and our parents.
Our bodies, scientifically, are impermanent during our life. Different than the were roughly six to nine months ago. Because of cell replication, old cells die off, new ones are created, and our skeletons even recycle themselves.
Thich Nhat Hanh says in his book, The Heart of the Buddha's Teachings, "Impermanence is what makes transformation possible." This is very true. How could we become enlightened or further ourselves if what we were (our habits, emotions, etc) were permanent?
It impermanence that helps turn suffering into joy.