The picture plane is the single most important principle of linear perspective, to my mind, and probably the one that is least referred to in most explanations of linear perspective.
It all began in early 15th century Florence when an artist and architect called Filippo Brunelleschi came up with a bizarre experiment, probably to prove how much better he was than his rival Ghiberti. In so doing, he rediscovered long-lost rules of realistic drawing that an art theorist of the time, Leon Battista Alberti, developed into a full theory of how an artist should perceive his world to create realistic art: "On Painting".
I have summarized the ideas in the drawing below.
Note the most important fact of the illustration: the artist is looking at his subject as if he were looking through a pane of glass. This “pane of glass” is called the “picture plane”. If we imagine a line going straight from the artist’s eye to his subject, that straight line is called the "centric ray”. He stands on what we call the “ground plane”.
As the artist looks at his subject, its smaller,
scale image is reflected by rays of light rebounding off the subject and
appearing on the picture-plane, where he can mark it there, just like you can
look out a window in your home and use a felt-tip pen to trace the outline of your neighbor's house on the
glass. If you replace that sheet
of glass with a sheet of transparent paper, you finish with – a realistic
drawing. And that's precisely how an artist works.
To complete our understanding of this illustration, note that where the picture-plane meets the ground plane is called the “ground line”, and that the artist's “field of vision” is usually thought to be about a 90° angle on either side of the centric ray. It is generally thought that a realistic picture can portray about a 30° angle on either side of the centric ray.