The "Ascended Empire" refers to the coalition of ascended beings inhabiting the Alfleheym dimension as refered to by the ascended Alterran named Lyran. According to Lyran, when the original Alterra ascended to escape death by the plague, they were conscripted into the "Empire" and those who refused to assimilate were killed. The same process happened when a number of Lanteans ascended millenia later.
The ramifications of this revelation are significant. It means that the ascended "Ancients" aren't fully in control of their own actions and answer to a higher power, that being the "Empire" and those that control it, loosely refered to as "The Originals."
Many different species make up the Ascended Empire, though all have transitioned to an energy-based existence in the same fashion and all inhabit the Alfleheym dimension with the ability to cross over into Midgar(our dimension). In this way they could be considered to be the same species(ascended) and homogeneous with the exception of the Originals who began their existence as energy-based lifeforms.
The "Ascended Rule-book" that Dr. Jackson refered to is in fact a list of edicts given to the Empire by the Originals. Should the Ascended Ancients break these rules, they would have to face the wrath of the Empire, if not an Original itself. The Ancients are both masters of their region of the Empire's domain and slaves to its will. Most former Alterrans and Lanteans have fully assimilated into the Empire, foresaking their former allegiances, but a small group of loyalists remain, hidden within the Empire waiting for a chance to strike back at those who destroyed their civilization.
According to Lyran, a loyalist, it was the Ascended Empire that created the plague that destroyed them. The Empire feared their growing technology and physical advancement and decided to 'pluck the weed' before it grew into a true problem.
The Ascended Empire did so again, as Lyran says, with the Asgard and their genetic deterioration, caused not by natural causes or artificial manipulation by the Asgard themselves, but by a bioweapon created by the Ascended Empire to mimic natural deterioration...thus hiding the cause and preventing a solution from being found. Such a weapon takes a very long time to implement, but given that the Ascended Empire is millions of years old at the youngest, time it seems is not a concern so long as the outcome is what the Empire desires.
When not confronted with a potential threat, the Ascended Empire ignores the Midgar dimension with disdain and makes interacting with its inhabitants taboo, with minor violations dealt with by the regional division within the Empire and not worthy of the Originals' attention. It was in this way that Orlin's punishment was handed down by other former Alterrans acting as part of the Empire rather than have the other species or the Originals involved. Though accountable as part of the Empire as a whole, the Ancients seems to have a certain amount of autonomy regarding regional matters so long as they don't pose a threat to the Empire.
The Ascended Empire is not infinite. It has borders that are as yet undefined, but cover many, many galaxies. This means that not all ascended beings are part of the Empire, such as the Ori.
Lyran noted that the Ascended Empire's border ran somewhere between Avalona(Milky Way) and Destra(Ori galaxy), and as such the Ori were not integrated into the Empire, but they were watched. Had they encroached on the Empire's territory they would have started a war, but by keeping their invasion of Avalona strictly to within the Midgar dimension, which the Empire all but ignores, they avoided direct confrontation.