Far away, in the heavenly abode of the great god Indra, there is a wonderful net which has been hung by some cunning artificer in such a manner that it stretches out infinitely in all directions. In accordance with the extravagant tastes of deities, the artificer has hung a single glittering jewel in each eye of the net, and since the net itself is infinite in dimension, the jewels are infinite in number.
There hang the jewels, glittering like stars of the first magnitude, a wonderful sight to behold. If we now look closely at any one of the jewels for inspection, we will discover that in its polished surface are reflected all the other jewels in the net, infinite in number. Not only that, but each of the jewels reflected in this one jewel is reflecting all the other jewels, so that there is an infinite reflection process occuring.
This symbolises our world where every sentient being (and thing) is inter-related to one another.
Avatamsaka Sutra

Monks, we who look at the whole and not just the part, know that we too are systems of interdependence, of feelings, perceptions, thoughts, and consciousness all interconnected. Investigating in this way, we come to realize that there is no me or mine in any one part, just as a sound does not belong to any one part of the lute.
Samyutta Nikaya, from "Buddha Speaks

You are me, and I am you.
Isn't it obvious that we "inter-are"?
You cultivate the flower in yourself,
so that I will be beautiful.
I transform the garbage in myself,
so that you will not have to suffer.

I support you;
you support me.
I am in this world to offer you peace;
you are in this world to bring me joy.

Whenever we throw something away, whether in the garbage can, the compost, or the recycling, it can smell terrible. Rotting organic matter smells especially badly. But it can also become rich compost for fertilizing the garden. The fragrant rose and the stinking garbage are two sides of the same existence. Without one, the other cannot be. Everything becomes a part of the garbage. After six months, the garbage is transformed into a rose. When we speak of impermanence, we understand that everything is in transformation. This becomes that, and that becomes this.
Looking deeply, we can contemplate one thing and see everything else in it. We are not disturbed by change when we see the interconnectedness and continuity of all things. It is not that the life of an individual is permanent, but that life itself continues. When we identify ourselves with life and go beyond the boundaries of a separate identity, we shall be able to see the permanence in the impermanent, or the rose in the garbage.
Present Moment, Wonderful Moment: Mindfulness Verses for Daily Living

We find that between the past and the future there is an extremely thin line-something that cannot really withstand analysis. Past and future exist in relation to the present. But if the present cannot be posited, how can past and future be posited? This is a demonstration of dependent origination.

We learn from the principle of dependent origination that things and events do not come into being without causes. Suffering and unsatisfactory conditions are caused by our own delusions and the contaminated actions induced by them.

All events and incidents in life are so intimately linked with the fate of others that a single person on his or her own cannot even begin to act. Many ordinary human activities, both positive and negative, cannot even be conceived of apart from the existence of other people. Even the committing of harmful actions depends on the existence of others. Because of others, we have the opportunity to earn money if that is what we desire in life. Similarly, in reliance upon the existence of others it becomes possible for the media to create fame or disrepute for someone. On your own you cannot create any fame or disrepute no matter how loud you might shout. The closest you can get is to create an echo of your own voice.
Thus interdependence is a fundamental law of nature. Not only higher forms of life but also many of the smallest insects are social beings who, without any religion, law, or education, survive by mutual cooperation based on an innate recognition of their interconnectedness. The most subtle level of material phenomena is also governed by interdependence. All phenomena, from the planet we inhabit to the oceans, clouds, forests, and flowers that surround us, arise in dependence upon subtle patterns of energy. Without their proper interaction, they dissolve and decay.
The Compassionate Life

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 neighbor--means destroying yourself in the long run. You need your neighbor. More prosperity in your neighbor, 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.
The Wisdom of Forgiveness: Intimate Conversations and Journeys

When the thought of the internal
And the external as 'I' and 'mine'
Has perished, grasping ceases
And through that cessation birth ceases.

When actions and afflictions cease, there is liberation;
They arise from false conceptions, these arise
From the elaborations [of false views on inherent
Existence]; elaborations cease in emptiness."
Nagarjuna

Inherent existence has never been validly known to exist; therefore, it is impossible for there to be any phenomenon that exists through its own power. Since it is experienced that mere dependent-arisings, which are in fact empty of inherent existence, do cause all forms of help and harm, these are established as existent. Thus, mere dependent-arisings do exist. Therefore, all phenomena exist in the manner of appearing as varieties of dependent-arisings. They appear this way without passing beyond the sphere or condition of having just this nature of being utterly non-inherently existent. Therefore, all phenomena have two entities: one entity that is its superficial mode of appearance and one entity that is its deep mode of being. These two are called respectively conventional truths and ultimate truths.
The Buddhism of Tibet