A focal plane is a flat location within an optical system at which an image is focused. If something flat is placed to coincide with the focal plane, the image is formed on it: e.g., photographic film, a CCD, or a screen for viewing, or within the eye, the retina. For a telescope, the focal plane is a (mathematical) plane at which light from each point in the object observed, that entered the telescope, is brought back to a single point (its focal point), i.e., the telescope focuses the image. The focusing can be accomplished with a lens or, as in a reflector telescope, a concave mirror. In the simplest case, the distance from the lens or mirror to the focal plane is the focal length.
No optical system produces a perfect image, one cause of imperfection (i.e., aberration) being that the focal plane may be close to flat (planar) but not completely. A reason for the complexity of optics is minimizing this. (A possible method of compensating would be a sensor, e.g., CCD, that is slightly curved to more closely match the focus.)
In a research telescope with multiple instruments, one may be selected by moving it to the focal plane. Possibly the instrument will have further optics to further adjust the image, producing a subsequent focal plane for processing. For example, a spectroscope may provide a grating, with the light divided by wavelength focusing on a subsequent focal plane. Furthermore, with the use of partially reflective mirrors or prisms, light may be split into multiple optical paths leading to different focal planes, so as to process the image in different ways.