Accretion rate is general term a measure of accretion, typically mass per unit time. The term may be used for any astrophysical example of accretion, e.g., stars, planet formation and black holes.
Regarding black hole accretion rates, a black hole's Eddington accretion rate is a maximum, the rate at which it reaches its Eddington luminosity. This is relevant to active galactic nuclei and quasars which are presumed to be the result of supermassive black hole accretion, and provide hints to the size of the black hole. It appears that such accretion was most widespread in the history of the universe during the period of maximal star formation: the peak star-formation epoch.
In weather (relevant to bodies such as planets and moons), the terms accretion and accretion rate are used for the growth of water droplets (or other liquid droplets) in the formation of clouds and rain.