Gliese 581 g has attracted attention because it is near the middle of the habitable zone of its parent star. That means it could sustain liquid water on its surface and could potentially host life similar to that on Earth. (The planet is expected to have temperatures around -37 to -12°C, however). If it is a rocky planet, favorable atmospheric conditions could permit the presence of liquid water, a necessity for all known life, on its surface.
However, given it's close proximity to it's parent star, it's expected to be tidally locked, with one side permanently facing the star, which could lead to extreme temperatures on both sides. An atmosphere would tend to transport heat and make the variations somewhat less extreme, with some models suggesting that if there is water on the surface, it may be in the form of a thick crust of ice, with a thinner area, or perhaps open water at the sub-solar point. If the atmosphere is thicker, a permanent patch of open water may be present, giving rise to an "eyeball Earth". Unfortunately, current technology cannot answer questions regarding the composition of the planet or its atmosphere, if any,