We examine the relationship between galaxies, supermassive black holes and AGN using a sample of 23,000 narrow-emission-line ('type 2') active galactic nuclei (AGN) drawn from a sample of 123,000 galaxies from the Sloan Digital Sky Survey. We have studied how AGN host properties compare with those of normal galaxies and how they depend on the luminosity of the active nucleus. We find that AGN reside in massive galaxies and have distributions of sizes and concentrations that are similar to those of the early-type galaxies in our sample. The host galaxies of low-luminosity AGN have stellar populations similar to normal early types. The hosts of high- luminosity AGN have much younger mean stellar ages, and a significant fraction have experienced recent starbursts. High-luminosity AGN are also found in lower-density environments. We then use the stellar velocity dispersions of the AGN hosts to estimate black hole masses and their [OIII]lambda5007 emission-line luminosities to estimate black hole accretion rates. We find that the volume averaged ratio of star formation to black hole accretion is approximately 1000 for the bulge-dominated galaxies in our sample. This is remarkably similar to the observed ratio of stellar mass to black hole mass in nearby bulges. Most of the present-day black hole growth is occurring in black holes with masses less than 3 x 10(7)M(3). Our estimated accretion rates imply that low-mass black holes are growing on a time-scale that is comparable with the age of the Universe. Around 50% this growth takes place in AGN that are radiating within a factor of five of the Eddington luminosity. Such systems are rare, making up only 0.2% of the low-mass black hole population at the present day. The remaining growth occurs in lower luminosity AGN. The growth time-scale increases by more than an order of magnitude for the most massive black holes in our sample. We conclude that the evolution of the AGN luminosity function documented in recent optical and X-ray surveys is driven by a decrease in the characteristic mass scale of actively accreting black holes.