A hypermassive neutron star (HMNS) is a neutron star with sufficient mass to collapse into a black hole, basically, more massive than the Tolman-Oppenheimer-Volkoff limit, that immediately collapses (e.g., well within a second). Rotation of such a neutron star can counteract the effect of gravity and delay the collapse. The term supramassive neutron star (SMNS or sometimes spelled supermassive neutron star) has a similar meaning: it is used for such an overly-massive neutron star, sometimes intended to mean "longer lived than a HMNS" and sometimes assuming HMNS to be a sub-type.
Such neutron stars are of interest because they may exist for a short time in the midst of a neutron star merger, and their short existence can affect the observable phenomena, both electromagnetic radiation and gravitational waves. GW170817's merger appears to be such a case. Such neutron stars also could be a source of some as-yet-unexplained phenomena, e.g., some gamma-ray bursts. They are also of interest because of the possibility that some might persist due to rotation, which has some potential for explaining other observations, including transients occurring if they eventually collapse.