A couple things are happening.
First, there’s a lot of radiation coming off the matter surrounding the black hole as it falls inward. That radiation isn’t coming *from* the black hole, but it helps us to see where black holes are.
Second, there’s radiation coming off of the outer surface, or ‘event horizon’, of the black hole itself. The mechanism which produces this radiation is a lot weirder. It arises from the microscopic quantum fluctuations which are constantly happening all over the place in empty space, which create a phenomenon called “virtual particles.” These particles are always created in equal-and-opposite pairs, and usually cancel themselves out before they have a chance to go anywhere, or affect anything, or be observed. But when the fluctuations happen *right* at the edge of the region where radiation can’t escape, sometimes they don’t cancel out. Instead, one half falls into the black hole, and the other half escapes. This is called “Hawking radiation.”
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