Explain the notion of light/electromagnetic waves/photons to a non-physicist A non-physicist asked me about special relativity. My explanations naturally were based on gedankenexperiments involving light. This forced the question: "What is light? It is particles, isn't? Or is it waves?"
I tried to put together the different aspects of light. I thought about


*

*Quantum mechanics (quantum wave packages)

*Quantum Field theory (abelian gauge field)

*Special Relativity (moves with the speed of light)

*Classical Maxwell theory (electromagnetic waves).


Unfortunately, it was very difficult to point out the relation between theoretical definitions and the world of experience.
To cut a long story short: Is it possible to explain satisfyingly to a layman what light is?
 A: You should both watch this video of Richard Feynman: https://www.youtube.com/watch?v=qjmtJpzoW0o
I think it applies to "what" questions as well. If you try to describe what a light is, you just end up replacing it by some different terms. Your friend then might not understand those terms and you will end up replacing them by even more terms and this cycle will eventually continue indefinitely. 
Physics describes behaviour of light - we can predict what will happen in your eye or what will be measured in some equipment given some circumstances, and that is enough for all practical purposes. All other things like "particles" or "waves" are our analogies, that just help us comprehend the equations. But it's in principle impossible to definitely describe what a light is, just as it's impossible to definitely describe what a rock is. You just have to accept existence of something at some level of undestanding.
A: 
A non-physicist asked me about special relativity. [...]
  I tried to put together the different aspects of light.

What's missing from your OP list is the "aspect" which is of paramount importance in the foundation (and thus, for explaining) relativity. Namely:
"light" in the sense of "exchanging signals"; specifically referring to the  "signal front".
This particular "aspect" and pre-requisit for understanding Einstein's theory of relativity I'd explain to a (by my prejudices typical) layperson so:

Imagine that you and your friends were sitting in a class room; each pretty much alone by themselves, tending their own business. And suddenly you got struck: by a good idea, or by a paper ball, or by having seen something exciting, for instance.
Then, after a while (perhaps only a very litte while) you first notice that some friend who had been watching you had first noticed that you had been struck. (You crack a smile just thinking about that. ;)
That's how you know 


*

*that your friend had received a light signal from you, and

*that you had exchanged a light ping signal with your friend.

That's pretty much what Einstein was referring to when writing about "light"; and, for all practical purposes, Maxwell and Feynman, too.
A: If your are willing to accept that we are surrounded be this thing called "the electromagnetic field", then light is an oscillation in that field, which propagates in the direction perpendicular to those oscillations (at the speed of light).
Light exhibits the characteristics of both waves and particles (because experiments taught us so:), so it can be referred to as a beam of light, or a stream\flux of photons.
Among the characteristics of light, is the frequency of the mentioned oscillations. These we experience as different colors seen by our eyes. 
A: The most important thing to understand is that light is not merely a particle or a wave, but a mechanism that has characteristics of both. Photons are not measured the way atoms and subatomic particles are, in which they are singular and point like, but they are measured as wave frequencies that only accept a certain amount of energy directly proportional to the frequency of the photon, much like how you can only fill a gallon jug so much until it can no longer fill anymore volume. However this analogy is a bit dodgy, since the gallon jug MUST be filled, and the larger the jug, the higher the frequency. If the photon cannot be filled, then the energy is simply transferred to smaller photon frequencies that can accept the energy.
This is exactly the way Einstein had predicted it to be. These photons travel constantly at the speed of light, therefore they are never at rest. Hence the reason why we say that light has no '"rest mass". Physics does not focus much on the inner workings of light, but focuses more on the actual characteristics in which we observe it in our everyday universe, such as observing quantum tunneling, entangling, superposition and famous experiments such as the Stern-Gerlach experiment, or Schröinger's cat. None of these explains WHY light behaves the way it does, but simply describes how it behaves, and from observing these behaviors, we can derive rates of change in a system and find out what is causing the system to behave the way that it is(Yes there are a high amount of photons here with strong electromagnetic properties, but what is causing it?), such as deriving electromagnetic waves from Maxwell's equations. They are essentially proofs that say yes, this is what is going on in the system.
A: 
What is light? It is particles, isn't? Or is it waves?"

We can never know what something really is. You friend surely knows light from experience. He may not know some of the peculiar phenomena that people discovered, like total reflection, diffraction, constant speed etc. You tell him story about these discoveries, show him pictures and how people tried to explain them - with particles, then waves, then particles, then waves, with perpetual surprisals and no final answer on the horizon.
A: Try to explain how light is a group of photons. Explain that photons are essentially particles but are so small that they act wavelike. If they ask more, refer them to the Wikipedia article about photons. It's fairly informative
