Looking for a clear explanation of "interdependent origination" in English (one that doesn't rely a lot of Buddhist terminology)?
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.