An eclipse occurs when one body obscures light from another body. The best known phenomenon of this type is a Solar eclipse, which occurs when the Moon passes between the Earth and the Sun, blocking the Sun's light from a region on the planet's surface. There is also the more common Lunar Eclipse where the full moon passes inside the Earth's shadow leaving it only lit by reflected Earth light.
Eclipse in Mass Effect
Eclipse was founded by an asari named Jona Sedaris. Little is known about the larger Eclipse network. Eclipse cells operate on various planets under the direction of a local officer, who supervises their operations. In addition to mercenary work, they are also active smugglers of weapons, drugs, and fugitives. A typical Eclipse cell is a commando unit that emphasizes the use of mobility, biotic powers, and combat engineering (tech powers).
Eclipse is a significant force in the poorly governed Terminus Systems, but their forces are far too limited to threaten a major planetary government, let alone an interstellar government.