It's a good idea Mirasol.
Vector drawings are made with objects (such as lines, arcs and circles) that are defined by coordinates and functions. Many softwares use that, like Corel Draw, Inkscape or more specialized things like CAD software (AutoCAD, Revit, etc...). But when we create a line or a circle in a word processor (Microsoft Word) or in a presentation software (Powerpoint) we are also creating a vectorial object. So you probably already did that many times.
By opposition our hand-made drawings aren't defined by any numbers or functions. When you draw a line it's "more or less" straight, depending of your ability, and a circle is approximately round, but as you know well it's not perfect.
So in a vectorial drawing a line will be a vector between two coordinates (x and y, and z if you want to go tridimensional), let's say a line from point 1,1 to point 3,4.
That line will be
absolutely straight (because
you said that you want a
line) and, more important, it will remain the same whatever the scale you look at it.
If you want a circle in the end of the that line you can say: Circle with center on point 3,4 and radius of 2. That circle will be a
perfect circle.
Vectorial objects also allow us to modify them (move, scale, rotate) without loosing anything in their nature, which is great. And you can also copy them as much as you want.
Purple Wyrm circles are, I'm quite sure, all the same size, with the same border width. And the lines that connect them are all similar too.
So vectorial is great for a lot of things. The only "setback" is that when you draw freely you don't have to be defining everything, the drawing just flows. It's not perfect but most times its much more expressive and natural.
I hope I helped!