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. Some lenses will advertise that they have low dispersion glass or "ED" glass on one of the elements - this is one thing that can help them design a lens that reduces chromatic abberation. Reducing chromatic abberation tends to involve compromise - there's no such thing as perfect as it would compromise on some other quality of the lens.
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.
Chromatic aberration is color fringing along the edges of things in your photographic image. It's caused by the optical design of the lens, and is a physical property of the lens.
It's caused when the glass refracts the light and can't get all the frequencies (colors) of light to coalesce together, physically, in the same spot on the sensor. IOW, it's sort of acting like a prism and splitting the colors apart. Typically, a more expensive lens has additional corrective elements to help eliminate this.
If the frequency split is side-by-side, this is known as lateral chromatic aberration (also called transverse CA), and you typically see blue/red "shadows" side by side. Post-processing can often eliminate this form of CA by realigning the different colors.
If, however, the split is front-to-back, this is known as longitudinal chromatic aberration along with a bunch of other names like "bokeh CA". In this case you more commonly see green/purple halos around subjects. It's very common as purple fringe with fast prime lenses shot wide open, and can be mitigated by stopping the lens down to a smaller aperture setting.