What is a x-simple and y-simple region?

Question

In Vector Calculus by Marsden, Tromba, and Freedman, they define something called $x$- and $y$-simple regions in the chapter about Green's and Stoke's Theorem:

I have read the definition, but I do not quite understand what it means.

Answer 1

A region $D \subset \mathbb{R}^2$ is x-simple ($y$-simple) if every horizontal (vertical) line intersects $D$ in a line segment.

For example, the unit disk is $x$ and $y$-regular but an annulus is neither $x$ or $y$-regular as a line through the middle of the annulus intersects at two line segments, not a singular one.