The plane of play is simply where the game play takes place. Since Catch! is fundamentally a 2d game in a 3d world, game play will only happen in a slice of that world.
Take a Large Spiral for instance. Since it is hardly flat it will intersect the plane of play in multiple places. This could allow for Throwable which is on the red plane of play to pass in front of, or behind the spiral relative to the player’s perspective. In this specific example the blue lines represent the 2d shapes that objects on the Plane Of play would interact with.
Spiral reference image: http://www.mathworks.fr/matlabcentral/fx_files/22377/2/intersect.bmp