The Eclipse were a mecenary group operating in the Terminus Systems, and though typically seen as less dangerous than the Blue Suns, they made up for it with both numbers and ruthlessness. They are recurring enemies in Mass Effect 2.
The Eclipse were founded by Jona Sedaris and operate almost exclusively in the Terminus Systems. There they perform all manner of crimes, with a specialty in drug trafficking, including the biotic enhancer Red Sand. Eclipse activity on the planets Omega and Illium are especially strong, but in the end several of the cells were wiped out by Commander Shepard and their allies during their fight to stop the Collectors.
In Mass Effect 3, the Eclipse can be potentially recruited in the war against the Reapers. Whether they will be led by their founder relased from prison by Shepard, or their more rational and even-headed second in command depends on Shepard's actions. Whether or not they survived to the end of the Reaper war is unknown.