An X-ray burster (sometimes what is meant by XRB) is a celestial object that produces very short bursts of X-ray (X-ray bursts, analogous to gamma-ray bursts) that appear in seconds or less and last seconds or less. The term X-ray nova (XN) is more often used for temporary X-ray sources that rise over the course of hours or days and analogously last longer, and the term X-ray flash (XRF) is used for bursts of X-rays showing a distinct set of characteristics, ascribed to a different source (core collapse supernovae).
X-ray bursters are presumed to be neutron star binaries, i.e., a binary star that includes a neutron star in which the neutron star is accreting material from its companion, and fusion is triggered on the surface, lasting only a moment. If the burst reaches Eddington luminosity, then radiation pressure can push the hot, glowing material outward, which is termed photospheric radius expansion (PRE). Analysis of such events offer information: they serve as standard candles, and the radius and mass of the neutron star can be estimated.
X-ray novas are presumed to be due to accretion on a black hole or neutron star from a binary companion. (I'm not sure of the emission mechanism, i.e., simply black-body radiation versus some non-thermal mechanism.)