The Film Plane
Film plane is a word that came about when actual physical film was used, but is still used in relation to digital photography. So, back when film was the standard, the film plane was the place where a small section of film was positioned to catch the incoming light.
The film plane is where light exposes that specific portion of film while the rest of the film is tucked safely away in the dark.
Film Plane in Digital Terms
With a digital camera it is more of a sensor plane than film plane because of there is no film, but rather a CCD Sensor. Just think of it as the place where the light hits the plane/sensor or film to capture the pictures you take.
During the exposure of light on the film/sensor the image is received onto the light sensitive film or translated into a digital image to view on your LCD screen.