The phrase "horizontal plane" refers to a flat surface or level that is parallel to the ground. It is a term used to describe a geometric orientation that is neither slanting nor vertical but runs straight and level. Full definition
Hanging light fixtures break up the mostly horizontal planes of a modern bedroom. (thespruce.com)
The shoulder button placement isn't ideal, as they're on the same horizontal plane as the existing shoulder inputs, which is unlike every other controller I can remember. (gamesradar.com)
A confident dashboard creates a strong horizontal plane for the driver to work. (kiamedia.com)