Accretion of gas onto a black hole provides the most efficient means known for liberating energy in the nearby universe. This is good for observational astronomers, since it allows regions close to the event horizon to be studied directly through emitted radiation. But it is also crucial for understanding the influence of black holes on galaxy formation and evolution. The huge amounts of energy released close to accreting black holes, particularly in the form of winds and jets, but also in the form of energetic radiation, can affect the thermal and dynamical states of matter out to large distances, making black holes important agents of change on cosmological scales.
Astrophysical black holes are described by two parameters that effectively set the inner boundary conditions for accretion. The mass, M, basically determines the characteristic length and time scales close to the horizon, whereas the Kerr spin parameter a / M (where a = J / M is the specific angular momentum of the hole, in geometric units G = c = 1), with 0 ≤ a / M ≤ 1, determines the efficiency of energy release and, coupled to the magnetic and radiative properties of the infalling gas, the forms in which energy is liberated.
Although the horizon (at RH) marks the point of invisibility and no return for matter being accreted by a black hole, the energy efficiency of accretion is determined somewhat farther out, near the innermost stable circular orbit (ISCO). A test particle orbiting inside this radius will be swallowed by the black hole without giving up any additional energy or angular momentum. Because RISCO decreases from 6 M (= 3 RH) for a Schwarzschild black hole to M (= RH) for a corotating orbit around an extreme (a / M = 1) Kerr hole, accretion is more efficient for a rotating hole than for a stationary one. (Note, however, that RISCO increases with a / M for counter-rotating orbits and approaches 9M for extreme Kerr, affording much lower efficiency.) The specific angular momentum corresponding to the ISCO decreases from 2√3M to 2 M / √3 as a / M increases from 0 to 1, and the efficiency of energy release increases from about 6% of M c2 to about 42%. Hartle's undergraduate textbook on relativity  provides a very readable discussion of these key features.