What is Chromatic Aberration? Is it a physical part of the lens, or just an optical illusion?
Chromatic Aberration is a distortion that occurs when a lens focuses different colours slightly differently.
It is caused by the refractive index of the lens (the amount that the lens bends light) being slightly different for different colours, so I suppose you could say it is caused by physical properties of the lens. It is possible to produce higher quality lenses that exhibit this effect to a lesser extent.
Wikipedia has a very detailed article on chromatic aberration.
When light enters or exits glass at an angle, it bends. But the different colours in the light bend by a different amount.
Lenses try to cancel this effect out with multiple opposing elements, particularly with different densities of glass, but they have to take compromises - there's no such thing as perfect as it would compromise on something else.
So you may still see colour fringes, particularly at the edge of your frame (where the light hits your lens at a greater angle) in some conditions (typically high contrast). The colour fringes will often be blue (or purple-ish) as blue light bends (refracts) more than other colours. You may also see colour fringes in out of focus areas (bokeh). Different lens designs will show this up differently.
If you're trying to figure out how to identify it in your photos, it's that faint purple halo that appears. It's usually easy to spot when shooting a dark object against a bright background.