A focal plane is a plane within an optical system where an image is focused. For a telescope, it is a plane at which light from each point in the object observed, if it entered the telescope, is brought back to a single point (its focal point) i.e., 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 in the eye, the retina.
The focusing can be accomplished with a lens or, as in a reflector telescope, a mirror. 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 designing to reduce and minimize 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, they may be selected by moving the instrument in use to the focal plane. Possibly the instrument will have further optics to further adjust the image and produce 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 to process the image in different ways.