Keeping it simple, what's the difference between NURBS and Polygons?

Really really simply, it’s the same as a difference between a bunch of line segments and a bezier curve in Illustrator, but in 3 dimensions.

This is off the top of my head (it’s been a while since I’ve done hardcore graphics programming)—but a Non-Rational Bezier Spline (NURB) is a way of representing a three dimensional shape as a mathematical equation—meaning you can have a very smooth curve instead of a bunch of discrete “points” (or triangles) that you have with a polygon.

NURBS are great for modeling curved surfaces—polygons are better suited for primitives or instances where you really need to mind the complexity of your model… like models for games—or at least that was important back in the 90’s.

Ultimately, everything reduces to polygons when you render… just like a vector curve rasterizes into a bunch of pixels.

Do that help you out?

in very simple terms:
NURBS works through bezier curves, whereas polygons work via single point vertexs