Monotheist Religious Institution
Monotheism is the belief in one omniscient and omnipotent god. They view the multiplicity of Colonial gods as false. Most of colonial civilization is polytheistic, but a minority is monotheistic. ("Pilot")
They believe in a more rigid code of ethics and morality than polytheists - they see the world in shades of "black and white" rather than shades of gray.
Repelled by the hedonism and barbarism of parts of colonial society (in particular the Virtual World), they have adopted as their mission to clean up the vices and sins of the worlds by sharing the word of the One True God. ("Pilot")
The Conclave is a governing body of leaders which meets at the Retreat. Church business and proposals are presented to them first. The Head of the Conclave then meets with the Mother to discuss the business. He is her trusted advisor. ("Unvanquished")
The Soldiers of the One is the military arm of the church. They commit acts of terrorism to bring attention to their faith. The Church publicly disavows them, but still relies on them to carry out covert operations. ("Pilot") ("Unvanquished")
The Monotheistic Church is located between two warring factions on Gemenon - the polytheistic rebels on the east and the Hephaestons on the other side. Diego, one of the Soldiers of the One leaders, says it is a big stalemate. ("Unvanquished")
Behind the Scenes
Earlier in the series, Monotheism and Soldiers of the One were confused as one in the same although they are not. Jane Espenson commented on this,
"We wanted to make a lot of effort to make really clear what the STO is, what its goals are, and how it fits into the larger Monotheist Church. Because we were finding that we were even getting confused in the [writers] room, that we were using the words 'monotheist' and 'STO' interchangeably, and they're not." 
"The Monotheist Church is much larger. . . and much more established and respectable. . . It's got some history behind it now."