What for? Vector illustration is a special kind of digital illustration. Vector images are drawn from math formulas translated into geometrical curves (as opposed to bitmap-based illustration, the approach taken by software like Photoshop, with which one actually paints with pixels—colored points of light). A vector illustration is a set of virtual geometrical shapes stacked (artistically?) one upon the other, almost like in a traditional kindergarten collage.

The most manifest advantage of vector-based illustration over bitmap-based illustration is that, since it's plotted from mathematical equations embedded in the image file itself, a vector illustration can be resized up indefinitely. You don't have to deal with that dreadful pixelation effect typical of a small photo enlarged in the computer.