The High Lords of Terra are the rulers of the Imperium, who act in the Emperor's stead while he is unable to speak.
Official Canon Edit
Each of the high lords represents a specific branch of the Imperial government, and while they are generally capable of running their own branches without much interference, they still need to convene on matters of policy that affect the Imperium as a whole. However, by the 41st millenium, they have grown into incompetent bureaucrats who tend to make things worse for the citizenry.
The incompetency of the High Lords had been known as early as the War of the Beast, when the various High Lords refused to do anything constructive, and some openly attempting to placate the Orks to maintain their power. Eventually they were all killed by the leader of the Officio Assassinorum in an event known as the Beheading.
TTS Canon Edit
While there are more members of the High Lords, the four that meet the most regularly are the Grand Provost Marshal, the Commander Militant, the Master of the Administratum, and the Fabricator-General. The four were picked up from the Old Folks' Planet to run the Senatorum Imperialis, though they spend most of their time making things illegal, such as breathing, and keeping laxatives for themselves. They're not actively malicious, they're simply unaware that laws could be used to benefit other citizens of the Imperium.
The High Lords were eventually made obsolete when the Emperor started speaking again, and eventually made it illegal for them to make new laws to put a stop to their antics. Magnus attempted to have them assassinated so that he could rule the Imperium in their stead, but the men that Kitten shot turned out to be Lacrymoles instead.
The Grand Provost Marshal is obsessed with the law, constantly shouting "I AM THE LAW!"
The Commander Militant seems to be the least senile of the bunch, as he's able to keep the interests of his generals and soldiers (and by extension, the Imperium at large) safe from the whims of his ban-happy peers. He is also a pimpin' gangsta in his spare time.
The Master of the Administratum is fixated on keeping his bowl movements regular, but otherwise isn't terribly inept.
The Fabricator-General always speaks in auto-tuned melodies and complains that his fellow High Lords don't have enough cybernetic modifications. He is unable to say "buttcheeks," as it causes him to self-destruct (though he will be perfectly fine in the next scene). And like his fellow Tech-Priests, he's obsessed with toasters.
Other High Lords Edit
Other members of the Imperium who count as High Lords are: