The Edo God was one of a group of powerful inter-dimensional lifeforms that claimed the star cluster around Rubicun and Strnad systems as theirs. One of their manifestations was a structure in orbit of Rubicun III, worshiped by the Edo, to whom they had revealed their presence and accepted their worship, as it did not consider this harmful to the Edo's development at that time. The lifeform considered the Edo its "children" and protected them from outside influence or threat.
The structure was partially detected by a starship's sensors, and was generally invisible. The structure was discovered by the USS Enterprise-D in 2364, while in orbit of the planet for possible shore leave. It appeared only when Data asked the object to reveal itself; even then, the structure appeared transparent, and sensors read it as "not entirely real". As Data surmised later, once they belonged to this dimension but evolved considerably; they occupied several dimensions, being in several places at once.
A spherical entity from the structure passed through the Enterprise and a voice inquired why the ship visited the planet and why Picard had left his own lifeforms in the Strnad colony. After demanding to not interfere with its "children", the sphere then stuck on Data's forehead, exchanging information with him. During that session, it had the ability to block communication with the Enterprise away team.
When Picard brought Rivan aboard the Enterprise from the planet, she recognized the structure as God, having appeared to them in the past. The structure then started a collision course with the Enterprise as the voice demanded that Rivan be returned.
While Wesley Crusher was held in protected custody awaiting execution, Picard worried about how they would react if he interfered with the Edo laws and violated their own Prime Directive. When Picard tried to leave the planet with Wesley, the entity blocked the transporter. It was convinced by a passionate speech from Picard (plus a profound, semi-rhetorical question from Riker: "Since when has justice ever been as simple as a rule book?").