Why is light called an 'electromagnetic wave' if it's neither electric nor magnetic? How can light be called electromagnetic if it doesn't appear to be electric nor magnetic?
If I go out to the sunlight, magnets aren't affected (or don't seem to be).  And there is no transfer of electric charge/electrons (as there is in AC/DC current in space). 
In particular, the photons (which light is supposed to be composed of) have no electric charge (nor do they have magnetic charge). 
I'm looking for an explanation that can be appreciated by the average non-physicist Joe.
 A: This image (taken from Wikipedia) demonstrates what an electromagnetic wave looks like. 

Changing electric fields induce a magnetic field (this is how electromagnets work), and changing magnetic fields induce an electric field (this is how the charger on your electric toothbrush works).  The result is that if one oscillates, so will the other, and they will continually induce each other. 
I hope that at least gives an intuitive explanation for it (even if some of what I said is not 100% technically correct).
A: Light is an oscillating electric and magnetic field, so it is electrical and magnetic.
Later: re the edit to your question, I think there are two issues. Firstly the interaction with electric charge and secondly the interaction with magnets.
Light does not carry any charge itself, so it does not attract or repel charged particles like electrons. Instead light is an oscillating electric and magnetic field. If you take an electron and put it in a static electric field (e.g. around a Van de Graaff Generator) then the electron feels a force due to the field and will move. This happens when an electron interacts with a light wave, but because the light wave is an oscillating field the electron moves to and fro and there is no net motion. If you could watch an electron as light passes by you'd see it start oscillating to and fro, but it's net position wouldn't change.
This is exactly what happens in your TV aerial. The light (i.e. radio frequency EM) causes electrons in the TV aerial to oscillate and this oscillation generates an oscillating electric current. The voltage this generates is amplified by your TV. At the TV transmitter the same happens in reverse: an oscillating voltage is applied to the TV transmitter, the electrons oscillate in response and the oscillation generates an electromagnetic wave. So the process is oscillating electrons -> light -> oscillating electrons.
I'm not entirely sure what you mean by there is no transfer of electric charge/electrons (as there is in AC/DC current in space). If the above doesn't satisfactorily explain what's going on maybe you could expand on your question.
And finally on to the interaction with magnets.
The big difference between electric and magnetic fields is that (as far as we know) there are no isolated magnetic charges. If there were isolated magnetic charges e.g. if you could watch a magnetic monopole as a light wave passed by then you'd see similar behaviour to an electron. But there aren't, so you don't.
A: Light is called an 'electromagnetic wave' for historical reasons* in the following sense: 
It turned out that the effects of visible light and other radiation can be calculated using Maxwell's equations, which are also used to model the behaviour of electrically charged particles. This was an instant of a successful unification and it hasn't been dismissed since. Nine answer and the word "Maxwell" has not been used yet! Please see also the following wikipedia article, which contains a section First to propose that light is an electromagnetic wave.
(*That bold sentence is essentially a tautology: People name things, and so names are not independed from previous experience. At least both the Descriptivist theory of names by Russel et. al. and the more modern Causal theory of reference by Saul Kripke exibit this feature.)
A: 
How can light be called electromagnetic if it doesn't appear to be electric nor magnetic??

But light does appear to be electric and magnetic in nature.  For example:
Photovoltaic effect:

The photovoltaic effect is the creation of voltage or electric current
  in a material upon exposure to light.

Focus: Measuring the Magnetism of Light

Now two groups have independently demonstrated that a tiny, metallic
  probe will interact strongly with the magnetic field of light waves
  trapped in a sort of semiconductor “box.”

A: To illustrate the magnetic effect of e.m. wave on matter my favorite example is to talk about the microwave. 
The microwave is a lamp but emits invisible light (lower frequencies). 
Every polarized molecule will oscillate if subjected to this field. 
The result is that the molecule (i.e. water) are oscillating (vibrating) and therefore the temperature increases (the temperature measures the average "speed" of molecules).
A: 
How can light be called electromagnetic if it doesn't appear to be
  electric nor magnetic?

According to the theory of Electricity and Magnetism, charged particles which are stationary are "electric", charged particles which move at a constant velocity are "magnetic", and charged particles which accelerates will emit "electro-magnetic radiation" which travels at the speed of light.
Charged particles can't interact instantaneously, but rather there is a field of energy which mediates their interaction.  This field of energy is what we call "the electromagnetic field'.
In other words, "light" is the transportation of energy from one part of the electromagnetic field to another, and it facilitates the interaction between electric and magnetic objects, but is neither electric nor magnetic itself.
A: Sound is a mechanical vibration, but you can only sometimes observe it making things vibrate. Sometimes the vibrations are too small, or too fast. The same kind of thing is true of light.
Visible light has a wavelength from about 400-700nm, far smaller than anything you can discern unaided. This corresponds to frequencies of about 4-7*10^14 Hz, far faster than anything you can perceive.
So yes, at a very small and fast scale, sunlight is composed of electromagnetic waves (oscillating electric and magnetic fields), and they do have elecromagnetic effects on things - they're just not usually visible effects.
But for example, radio is also electromagnetic radiation (with much longer wavelength and lower frequency than visible light), and it has electrical effects, so an antenna can convert between radio waves and oscillating electrical currents.
Magnetic effects are a bit tougher to observe. Perhaps the most commonly known one is the Faraday effect - magnetic fields can rotate the polarization of light.
A: Light is a propagating electromagnetic field disturbance. If we ignore certain obscure quantum effects, light is not bent by electric or magnetic fields because it does not carry charge particles. The field disturbances simply superimpose onto whatever electric and magnetic fields are permeating the traversed space.
A: As others have pointed out, light is actually both magnetic and electrical. It is part of the electromagnetic spectrum, which has everything from invisible light such as gamma rays, infra red and xrays to the visible light that you speak of. 
A: As light is produced by the acceleration of charged particles & from law of electromagnetism that states that: an accelerated charge produce electromagnetic wave,light is an electromagnetic wave. Actually light is the transfer of energy from one part of electromagnetic field to other. Everyone knows how the electromagnetic wave looks like(see answer by asmesure). As electric and magnetic field are perpendicular to each other they behave as crossfield but it does not mean that the charged particles feels no net force.They do feel some force, that is why charged particles oscillates by passage of electromagnetic wave.But their amplitude of oscillation is very small. So we don't see or feel charged particles affected by light though its electromagnetic. However light facilitates the interaction between electric and magnetic objects.? 
