A binary SMBH (binary supermassive black hole or BSMBH) is two co-orbiting supermassive black holes. Other terms found in publications: SMBHB for SMBH binary or supermassive black hole binary and SMBBH for supermassive binary black hole.
The concept is of interest because gravitational waves they would produce may be detectable, e.g., through pulsar timing arrays. Galaxies merge, typically each hosting a SMBH, and it is theorized that their respective SMBHs can fall into orbit. The resulting gravitational waves could become detectable if the orbit tightens sufficiently.
When the black holes orbit, the energy loss from gravitational waves draw them together, i.e., a black hole merger, but above a certain distance apart, this would be taking too long, e.g., longer than the age of the universe. Tightening the orbit, and even entering orbit necessarily requires interaction with other masses. Dynamical friction from stars explains a decline in orbit size to a point, but not sufficiently close to continue. The final parsec problem is the question of how the orbit might continue to tighten while within the gap between these two influences.