Super-Earth (or Superearth) is a common term for Extra-Solar Planets more massive than the Earth but substantially less massive than Uranus and Neptune, basically 2-10 Earth masses though there is no consensus on exact limits. What is considered a super-Earth generally has on the order of 1% of its mass as Atmosphere.
Usage regarding the planet's constituents and structure varies. Sometimes it is only meant to indicate the mass, even if the planet has a large atmosphere in the manner of a Gas Giant. In other instances, it is meant specifically to refer to Rocky Planets like Earth, in which case other terms have been used for Gas Planets of such a mass, such as Mini Neptune, Sub Neptune, Gas Dwarf, Mini Gas Giant, or Transitional Planet for planets with large atmospheres in the manner of Neptune, etc. The term Super-Puff means essentially a larger-than-Earth (super-earth) rocky core, but with a large, non-Earth-like atmosphere.
Current statistics and analysis suggest super-Earth's are very common, perhaps the most common type of planet. Some models suggest the larger ones would naturally experience runaway Accretion and become gas giants, and the fact that they didn't suggests the gas supply was cut off, i.e., the disk (Transitional Disk) dispersed after a short lifetime.
55 Cancri e (55 Cnc e)
GJ 1214 b