A black hole has a gravitational pull is so intense that nothing, not even light, can escape it once inside a certain region called the event horizon. As gas and dust (or even entire stars) are sucked in, the material is accelerated and heated to very high temperatures. This in turn results in the emission of X-ray light. Black holes containing lots of nearby gas and dust, such as this black hole at the center of the M81 galaxy, produce tremendous amounts of X-ray light.
Image Credit: X-ray: NASA/CXC/Wisconsin/D.Pooley & CfA/A.Zezas; Optical: NASA/ESA/CfA/A.Zezas; UV: NASA/JPL-Caltech/CfA/J.Huchra et al.; IR: NASA/JPL-Caltech/CfA