An X-ray binary is a close binary system where a neutron star (or more rarely a black hole) is accreting matter from what is usually a main sequence star. It is a very similar scenario to that which gives rise to cataclysmic variables, with the neutron star or black hole replacing the white dwarf as the primary star.
X-ray binaries are some of the most luminous X-ray sources in the sky. The X-rays are produced as material from the companion star is drawn to the compact object either through Roche-lobe overflow into an accretion disk (low-mass X-ray binaries) or through direct impact of a stellar wind onto the compact object (high-mass X-ray binaries).
In the Galaxy, X-ray binaries are primarily found in the galactic plane.