Phil Plait at Slate gives a bit more detail:
As the material swirls around the black hole, it emits X-rays at a very specific energy—think of it as a color. But as it orbits that color gets smeared out due to the Doppler effect. The amount of smearing indicates how fast the material is moving, and that in turn can tell astronomers how fast the black hole is spinning. This can be complicated by the presence of dense clouds of material farther out from the black hole that absorb X-rays and mess up our observations. The new data from NuSTAR allowed astronomers to show that the smearing seen is definitely due to rotation and not obscuration, unambiguously revealing the black hole's tremendous spin: just a hair below the speed of light!
Most black holes spin far slower than that, so something ramped this hole’s spin way up. One possibility, as I mentioned above, is material falling in over time. Another is that it ate one or more other black holes, which is creepy but possible. Galaxies collide, and when they do their central black holes can merge, growing larger. If the geometry is just right, this can create a single black hole with more spin. Due this a few times, and you can spin one up to fantastic speeds.
I’ll note that NGC 1365 is a massive galaxy, easily twice as large as the Milky Way (an we’re one of the biggest galaxies in the Universe). That’s exactly what you’d expect from a galaxy that’s spent a lifetime eating other ones. Cosmic cannibals grow fat when the hunting’s good.
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