A galaxy's surface brightness profile is the curve describing its brightness (intensity) from the brightest point (generally the center) to the edge, i.e., a function of the line of a radius, as the galaxy appears from Earth. It implies the galaxy's brightness is circularly symmetric, which is often somewhat close to true, but it can be cited as for the average value. The term is used for the observed surface brightness of a galaxy, which might be plotted based upon data, and is used for models, i.e., functions that approximate observed surface brightness of classes of galaxies.
A basic type of model is an exponential profile, that the brightness matches an exponential function of the distance from the brightest point. Another type is a de Vaucouleurs' profile in which brightness matches an exponential function of the 1/4 power of that distance. The Sérsic profile is a generalization that includes both, i.e., using the 1/n power of that distance, typically with a some n chosen from the range of 1 to 6 or so. The defining equations are often arranged so that the central brightness (or some other defined brightness) can be plugged in as well as a scale length, i.e., the distance over which the brightness falls by a factor of e.
Sometimes two such model profiles are used in combination, i.e., summed: for example, including a distinct profile to accommodate a galaxy's bulge.