Looking for a clear explanation of "interdependent origination" in English (one that doesn't rely a lot of Buddhist terminology)? I am having difficulty understanding the idea of interdependent origination within the following text. It is from The Essence of Buddhism by Traleg Kyabgon. I am finding this book very useful as a refresher on the basic philosophy of Buddhism, especially because it includes Tibetan Buddhism. However this section, which talks about one of the two main ideas in Buddhism, seems to rely on terminology that gives me the impression of circular reasoning. 


  "How, then, do things come into being? They come into being because of
  what is called interdependent origination, or pratitya-samutpada—that
  is, due to causes and conditions. This implies that things do not have
  inherent existence, because if they had any kind of essence or
  independent existence there would be no need for the whole idea of
  causality. Nagarjuna says: “The origination of inherent existence from
  causes and conditions is illogical, since if inherent existence
  originated from causes and conditions, all things would thereby become
  contingent. How could there be contingent inherent existence? For
  inherent existence is not contingent; nor is it dependent on another
  being. So the very idea of causality involves the notion that things
  are contingent. There is no being that can exist on its own without
  depending on anything else; no self-sufficient being. Everything is
  interdependent. Everything that exists on both the physical and mental
  plane involves the idea of interdependence, or pratitya-samutpada.”


I would very much appreciate an explanation, in clear English and without reliance on terminology (because it appears to be explaining by self referencing concepts and terms) of this basic idea. My guess is that the author is assuming that I already know something which I do not. References to online sources would be appreciated, if you can explain it yourself that would be terrific, and most of all if you can refer me to a clear, translation of the Buddha's original words about this that would be splendid. 

Many thanks.
The Wikipedia entry on dependent origination is pretty good and simple. Similarly there is a good essay called Dependent Arising by Piya Tan.

In simple terms this is as follows:


When the cause is present, the effect arising from the cause is present as well
When the cause arises, the effect arising from the cause arises as well
When the cause is not present, the effect arising from the cause is not present as well
When the cause ceases, the effect arising from the cause ceases as well


The 12 links dependent origination (found in numerous Suttas like (Avijjā) Paccaya Sutta) you fill in specific cases and their resulting effects and how these affects in turn become a cause to create more effects. 

The most elaborate of specific cause and effect relationships are found in the Theory of Conditional Relations. This maybe above the head for many.

Another rendering of this is the 4 Noble Truths.