A path is a line with zero or more curves, finite length, and zero width.

A stroked path is a path with a non-zero width.

Stroke expansion is going from a path to a stroked path.

Turns out that the math is quite complex.

I'm in search of a precise and consensus definition of a path with non-zero width... does anyone know where that is in the svg spec?

Imagine basic graphics program. Stroke expansion is how you go from a line drawn with a pencil to the one drawn with some brush.

It's how you go from drawing 1px width line to drawing paint covered area left by some brush following this line.