'Hypabyssal' is a geological term used to refer to igneous rock that formed underground ('intrusive igneous rock'), but cooled so quickly that fully developed large-grained minerals were unable to form. This gives it the appearance of volcanic rock ('extrusive igneous rock'), and indeed, these formations are often found in sub-volcanic vents. These formations are sometimes called by the less cryptic term subvolcanic rock, although technically any rock under the base of a volcano might be called subvolcanic.
Any magma that cools quickly might form hypabyssal rock, and so it is also found in narrow dikes and sills. Any igneous rock with a texture intermediate to large-grained (phaneritic) and small-grained (aphanitic) rocks may be considered hypabyssal. These formations are still considered to be a type of pluton.
Although the word 'hypabyssal' is formed from the roots hypo- and abyssal, is has no particular relation to the oceanic abysses.