The description of the word you requested from the astronomical dictionary is given below.
The surface brightness of a thing is the amount of light that you receive from it per unit solid angle. In astronomy, surface brightness is often measured in magnitudes per square degree, which is the magnitude of a star of which you'd receive as much light as from a square degree of the surface of the thing. The surface brightness does not change with distance or (if you have perfect optics) with the magnification of the telescope.
The surface brightness of the Sun (and hence also of most other things with a surface temperature of 5700 K) is about 10.9 magnitudes per square second of arc. The surface brightness of a typical galaxy is about 20 magnitudes per square second of arc.