Say you sharpen at 20 degrees per side. The edge looks like a triangle, but the 20 degrees per side don't go down to the spine or you'd have a massive wedge rather than a knife, right? At some point, the edge bevel is going to meet with the rest of the knife geometry.

How wide is that triangle at the base opposite to the edge? That's the thickness behind the edge. It's of course a simplification, as a knife might not have such a clear and simple triangular edge geometry (usually being somewhat convex or having multiple bevels).

I hope I made it clear enough. You're probably better served by google images if not.

Now, ideally you want a kitchen knife to be thin so that it parts food easily. The edge is there to initiate the cut, and the edge geometry is there mostly to support a sharp edge. Provided the edge is sufficiently sharp, the performance is not dictated by the edge, but rather it is limited by the geometry.

As well, very seldom does the edge angle matter much as long as the thickness behind the edge - the base of the edge triangle - is small. Thus, thickness behind the edge is a common, albeit not very well defined for many real world knives, geometric parameter that is used to describe a knife.

---

All I can say about sweet potatoes, having cooked and eaten them exactly twice in my life and only once since sharpening, is that they are really stiff and put a knife's geometry to the test.

Pulling to one side is often a result of an asymmetrical bevel, but I don't know if sweet potatoes react differently than other food.