Orientation comes in 3 flavors. Centered (the window is placed in the center of the mat) Portrait (the window is taller than it is wide). Landscape (the window is wider than it is tall).
Centered windows allow you to turn the mat in any direction and the window will be just fine. So it can be used for both vertical and horizontal pictures.
Portrait mats have a vertical image. Because the mat has a larger Bottom Margin than the Top Margin, the mat can only be used with a vertical image.
Landscape orientation has a horizontal window. It can only be used with a horizontal image because the Bottom Margin (the distance from the bottom of the mat to the window) is larger than the Top Margin (the distance from the top of the mat down to the window).
For those of you who want a PHD is this subject you can consider that a mat could be a portrait mat with a landscape window, a portrait mat with a portrait window, or a landscape mat with a portrait window, a landscape mat with a landscape window or you could simply purchase a centered mat and go out and buy a frame that can hang either way!
Riddle: What is a mat that doesn't have a window? A Back!