Hello Brian,

there is no deeper understanding needed. If you want, start with the simplest form of a curve - a line with start and end point (P0,P1). You can describe every point of the curve by a parameter u in this form: Pm(u)=(1-u)*P0+u*P1 with 1-u;u as weight/blending functions. The sum of both is always 1.

Now take a second line with P2,P3
Pn(u)=(1-u)*P2+u*P3

Now create a line between the curves with a parameter v:

PS(u,v)=(1-v)*Pm(u)+v*Pn(u)

This describes a ruled surface, better a point on it.
If one parameter is constant and the other is variable, you describe a iso curve. If you use more points and want to use Bezier have a look to Bernstein polynoms ---- 1-u;u are basic ones. If you want to use other e.g. spline you have to use different ones.

Have a nice day
Karsten
p.s.: No magic, nothing mystic - very simple vector math, but some of the guys try to give it a special flavour with mystic math symbols!