X-rays are generated by BH-star binary systems from a thermalized accretion disk. This process produces soft (low energy) X-ray radiation. In some systems, the high energy emission is much harder then that of a thermal disk and dominated by synchrotron X-rays emitted from shocked gas in the jet.

The Chandra X-ray Observatory caught two waves of hot, X-ray emitting gas emanating from the supermassive black hole at the center of NGC 5195. Image via NASA/CXC/Univ of Texas/E Schlegel et al.

Black holes are formed from collapsed supermassive stars. If a black hole ends up completely isolated then it will be very black. However, many stars are binaries. Moreover, within dense globular clusters stars can often pass very close to other stars. Just as with stars, when a black hole is near enough to another star it can collect matter from it. Black holes are incredibly compact objects with radii of only about 3km per solar mass. As matter falls onto such a compact object it will accelerate to high speeds and also be constrained to travel through a small volume of space, causing it to have a high chance of colliding with other matter falling into the black hole. This process creates an orbiting accretion disc of matter spiraling into the black hole. This matter is travelling so quickly and compressed so much that it is raised to enormous temperatures, so high that it emits a significant amount of energy as high energy EM radiation such as x-rays. Indeed, this process is by far the most efficient known process of converting matter to energy (an order of magnitude more efficient than nuclear fusion).

https://physics.stackexchange.com/questions/24958/how-can-a-black-hole-emit-x-rays