I am seeing in various places in the API documentation entities called U and V. An example of this is IFace2.IGetUVBounds. It returns the minimum and maximum of U and V for the face. Another method is IFace2.GetClosestPointOn. It returns the closest point in X, Y and Z space and also returns U and V.

I have found some tutorials from other cad software packages that look like U and V are a projection from some sort of flat plane. I don't want to assume though. I have also found some definitions of surfaces as a function of X, Y and Z based on a U, V value.

What is U and V?

In a simple term you can consider UV as a coordinate system in the face space (usually relative values). So for the flat surface U and V will range from 0 to 1. Look at the image in this article: Untrim face or surface with temporary geometry using SOLIDWORKS API

UV boundaries would allow you to find relative positions in the surface and to do something like ISO curves

This concept a little bit more complicated, but it should give you a general idea.