The theory of interdependence allows us to develop a wider perspective. With wider mind, there is less attachment to destructive emotions like anger, therefore more forgiveness. In today's world, every nation is heavily interdependent, interconnected. Under these circumstances, destroying your enemy--your neighbour--means destroying yourself in the long run. You need your neighbour. More prosperity in your neighbour, you'll get the benefit.

Now, we're not talking about the complete removal of feelings like anger, attachment, or pride. Just reduction. Interdependence is important because it is not a mere concept; it can actually help reduce the suffering caused by these destructive emotions.

We can say the theory of interdependence is an understanding of reality. We understand that our future depends on global well-being. Having this viewpoint reduces narrow-mindedness. With narrow mind, one is more likely to develop attachment, hatred. I think this is the best thing about the theory of interdependence--it is an explanation of the law of nature. It affects profoundly, for example, the environment.

--from The Wisdom of Forgiveness: Intimate Conversations and Journeys by His Holiness the Dalai Lama and Victor Chan

A simple example of how interdependent our society is:

Imagine purchasing a pair of prescription glasses.  The glasses are made up of the metal frame; the protective coating over the metal frame where it sits on our ears; screws to keep the frame together; silicone pads to cushion the frames on our noses; the glass lenses.  Now think of all of the people it has taken to make those one pair of glasses.  Really think about it. 

The people who mined the raw materials and then refined them into a usable form. 

The people who were involved in the transportation of every component, throughout every stage of the manufacturing process. 

The designer of the frames, lenses, the screws and the pads. 

The optometrist who tested your eyes to determine the type of lens you required.

The staff at the optometrist who also served you. 

Then there is the builder of the building that the optometrist conducts his business in. 

The people who were involved in manufacturing the equipment that the optometrist uses.

The people who trained the people who did all of the prior things mentioned. 

I could go on, but I think you get the point that the number of people who have contributed to that one pair of prescription glasses is unimaginable and they come from all over the entire planet.

That was only one small example; now stretch it out to include everything you have around you and every service that you use.  The ultimate conclusion is that we depend on each other so we should respect each other.