The picture plane is an imaginary plane (flat surface) which corresponds to the surface of the canvas (but sitting above it), directly at the viewer’s line of sight. It's commonly associated with the foreground of a painting, just at the viewer's line of sight.
Image the painting as being a flat structure sitting directly on top of a two dimensional canvas, which the artist manipulates (using shapes, lines and colour/placement, size, overlap etc) to create a sense of three dimensions.
Conceptually, the picture plane acts as a transparent window into illusionistic space. A simple way to think of how this works is to look through a window of your home. The view is 3 dimensional, framed either by your door or window. If you wanted to represent this as a picture of that scene, you would need to ensure that you created the sense of relative proportion, and the feeling that if you opened the window or door, you could travel through it into the world beyond.
In most representational paintings, all the elements in the picture appear to recede from the picture plane (ie behind it), while trompe l'œil effects are achieved by painting objects in such a way that they seem to project in front of the picture plane.
However, a number of modernist painters deliberately chose to present three dimensional objects as having the same flat surface (picture plane) as the canvas itself. You'll see this mostly in the period of Post-Impressionism onwards.
Jean-Louis Ernest Meissonier, Street Scene near Antibes, 1868
In this traditional, representational painting by Jean-Louis Ernest Meissonier there is a real sense that this is a 3 dimensional scene.
It is clear that the woman and child are standing in front of the man with the donkey and that the buildings are quite large on the sides and in the background.
There is also the sense that you could walk through the archway into a valley beyond.
Here the picture plane is designed carefully to provide a realistic description of the scene.
This work by William Michael Harnett is known as a trompe l'œil painting.
Instead of receding into the background, it appears that the violin is sitting on top of the picture plane. It looks to be a solid 3 dimensional object, along with the other objects 'sitting' on the shutter.
The effect is created largely by careful use of shadows, and also the sense that the viewer is looking straight at the objects.
William Michael Harnett, Still life Violin and Music 1888
Paul Cezanne, Still Life with Apples, 1890-94.
Cézanne's still life has quite a different effect. He felt that the illusionism of perspective denied the fact that a painting is a flat two-dimensional object. He liked to flatten the space in his paintings to place more emphasis on their surface - to stress the difference between a painting and reality. He saw painting in more abstract terms as the construction and arrangement of colour on a two-dimensional surface.
Still Life with Apples looks flat and distorted, as if he is wanting to show each of the objects within his vision, without trying to suggest any depth in the painting.
To achieve this he has made the back of the table wider than the front, which brings the back of the table forward to the foreground and pushes the front of the table toward the back. There is no real sense that the table recedes into the background, it's all at one level - as if the picture plane is just a flat surface.
When Cezanne started to 'see' art in a different way, it opened up many new ways of painting for the avant -guarde modernist painters who followed him.