Locally, there is a large amount of gas and dust attracted by the black hole's gravity. As this material approaches the black hole, it swirls in a vortex, like water swirling down a drain. As the material is packed together and falls into the hole ( passing inside the Swarzchild radius when we can no longer see what happens to the material) it emits large amounts of radiation. This, plus re-emitted light as this radiation heats up surrounding gas and dust, is visible as a bright shell or disk around the black hole.
However most of the brightness apparent at the center of a large galaxy is not at the very center. Galaxies are huge, and the density of stars tends to be greater towards the center of the galaxy. Therefore a line of sight towards the center of the galaxy will likely contain thousands of stars and therefore appear bright.
Answered by: Rob Landolfi, Science Teacher, Washington, DC
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