A subgiant star is brighter than a normal main sequence star (of the same spectral class) but not as bright as a giant star. They are post main sequence stars undergoing the same type of increased luminosity and radius as a giant star, but less so. They are generally slightly more than solar mass.
Some somewhat-low mass stars (e.g., the Sun) have a phase in their stellar evolution when they fit this fit this category. The phase, termed the subgiant branch (SGB), is their time transitioning from the main sequence to the red-giant branch.