I never asked for this, but rather for a clear overview of the models that exist, and where they fail. I understand it's experimental, and what interests me personally is (a) how can I use the existing models to do other fun things like write simulations and (b) where do the models break down so I can be more informed about the open directions in physics, which are almost always mathematical (what mathematical model describes the observations we see? how can we design an experiment that confirms or refutes a given mathematical model? etc.).
"What is light?" garners a very nebulous answer because there is a wide range of phenomena called "light" and work done in understanding what light is. "What is light in a fiber optic cable?" is more specified because it specifies a length (and thus wavelength) scale, an energy scale (not high intensity that makes you have to worry about plasma generation), and a time scale (steady state physics which allow talking about modes (ie., fourier analysis), unless you care about transients). The length scale and time scale rule out quantum mechanics, and probably will lead you to essentially to solving Helmholtz, which will be much more your speed. See, you might not know to specify all those scales, but by asking for a specific example, your physicist friend will restrict their universe of discourse down instinctively to a model you could use.
So light may be a bad example. The same could be said if you ask, "what is gravity" or "what are magnets?". Better questions are like, "how do we understand orbits in the solar system?" or "why do magnets stick to refrigerators?"
What about how exactly do people predict how likely it is the orbit of an asteroid/comet will intersect that of the earth? That is a very interesting problem. It is not at all solved as well as it could be.
First homework, reproduce the JPL HORIZONS ephemerides in your own way: http://ssd.jpl.nasa.gov/horizons.cgi
Second homework, improve upon this either in accuracy or efficiency.
Modern physics, so far as anyone has explained it to me, seems to be two partial responses to the results of that experiment (and the behavior of their test device, the interferometer) that we're in the process of synthesizing in to one result.
Wikipedia reasonably outlines the main features that modern physics has to account for, and links out to the two main bodies of work.
The problem is once you get away from those broad properties the model has to satisfy, there's several competing inplementations with somewhat different features/explanatory power.
Not saying they shouldn't teach past methods.
There are two kinds of people that fight actual Physics from within, those that say Math is not important: physical intuition "has to" be enough, and those that say that it's just Math, so they are equally happy with perfectly reasonable correct models and completely absurd correct models. They churn out both, usually more of the latter. Both schools of opinionated thought miss that wherever you go you have to learn the trade and be humble.
They should have told you that we don't know what things are, we just deal with how they do their thing.
It's a wave, it's a particle... it's a state, a linear combination of the eigenstates of the EM Hamiltonian, which span a Hilbert space. That's what we got and every physicist knows it, they are just being polite. If they told you that, your next question would be: why on Earth would you think that? why not just [random brainstorming here]? I don't think you're really interested in the really long answer, but it has to do with the boring fact that Physics is, above all, an experimental science.