I've been asking myself this question lately - it has become a kind of koan. I think early on in my love-affair with Buddhism I answered this question quite differently to how I would answer it now. Dependent Arising is the most important idea in Buddhism. Of course as Buddhists we say that mere words and concepts cannot completely encompass this central Insight of the Buddha, but in conceptual terms Dependent Arising is the sine qua non.
When we discuss this concept Buddhists often make the point by using examples from what I've been calling the objective pole of experience. That is to say we use examples from the world of objects that, from our dualistic points of view, appear to exist independent of us. I don't have a problem with positing objects in this way. There is quite a broad consensus amongst people in their right minds that there are objects, and I have no certain proof that there are no objects. So for instance we might illustrate dependent arising by using a traditional simile involving a chariot: it has wheels, an axle, a frame, a yoke, etc. Without all the parts assembled in the correct order the concept 'chariot' doesn't occur to us (there's a clue here to what I'm going to say next). Things, we say - implying objects - depend on causes, otherwise things don't exist.
One might complain, as I sometimes do, that not much change is visible in some objects. On my desk I have a sphere of polished crystal which has not perceptibly changed in many years. Some clever Buddhists answer that the crystal is busy changing at the atomic and sub-atomic level. But we must be careful about explaining Buddhist doctrine in scientific terms because such observations were not available to the Buddha. The Buddha had no knowledge of atoms or electrons or any of that. I prefer then, despite my scientific training, to try to explain the idea in terms that the Buddha himself would understand and use.
The problem disappeared for me one day when I was discussing this apparent difficulty with a friend. I observed that the huge chunk of rock towering over us had not perceptibly changed in several weeks of watching it. "Close your eyes", my friend said. Which I did. "Has your perception of the rock changed?", he asked. And of course my perception of the rock had completely and utterly changed from one of a sight experience to one of a memory experience. So here is the rub. Objects themselves may not be changing that much, but our minds our changing constantly.
The idea was powerfully reinforced for me by Professor Richard Gombrich when, during his 2006 Numata lectures, he emphasised that dhammas, the basic elements of the world from in Buddhist doctrine, are mental phenomena. I would now say that dhammas are the constituents of experience - they are to the mind, what forms are to the eye, or sounds to the ear.
So I would now say that what arises in dependence on causes is dhammas. This is to focus on what I tend to call the subjective pole of experience. I do not deny that objects are experienced, and that there is frequently a consensus about the existence of objects. But what we know about objects is mediated by the senses and the mind. There is no way around this - all information that we have about any object is via the senses and the mind. This leaves open the ontological status of objects - they may well be real, but we have no way of proving this. Equally we have no way of proving that objects are not real, and the consensus about the experience of some objects suggests that they are not particular to individuals in most cases. If two people agree that there is an object then it would seem to be independent of either person. It gets tricky however because my information about what your information comes to me via my senses. There is no way around this basic fact.
The Buddha described the unenlightened as obsessed by, and intoxicated with, the objects of the senses. In his last words he says that it is through appamāda that one attains [awakening]. My analysis of the etymology of the word appamāda, as well as how it is used throughout the Canon, is that it means something like "not blind-drunk on the objects of the senses".
The practical implication of focusing on dependent arising as referring to the arising of experience is that one can lessen the obsession, can sober up and see what is happening more clearly. When the Buddha says that all compounded things are impermanent and impersonal he is not, I think, referring to objects but to experience. He says "all compounded things are impermanent", but compounded things are known to be made up of dhammas and as I have said, dhammas are the elements of experience. It is experience which is impermanent, rather than things, although it is also true that things are impermanent. It is experience which is impersonal, and experiences which are unsatisfactory.
image: moonrise by Synapped