In the strictest sense, a super earth is just a planet with more mass than Earth, but less than a larger planet like Uranus or Neptune. So, super earths made of rock and metal, or even ice and gas. These planets could have oceans and atmospheres, or made of nothing but hydrogen and helium. The goal, of course, is to find a rocky super earth located in the habitable zone. This is the region where the planets are the right distance from the star for liquid water to be present.
The first discovery of a potentially habitable super earth was in the star system Gliese 581.
Here, astronomers found 2 planets orbiting within the habitable zone. Gliese 581 c has a mass of 5 times the Earth, and orbits on the overly warm side of the habitable zone and, Gliese 581 d is 7.7 times the mass of the Earth, and is on the cold side of the zone.