Okay. A brief run down.
Imperium - the empire of humanity. Founded by the God Emperor, who, funnily enough, promoted atheism throughout his walking life. However, this was to weaken the Chaos Gods, not because he didn't believe they existed. Allied with the Adeptus Mechanicus and the Adeptus Astartes, who are not, however, under their control. They have control of the Imperial Guard, who range from conscripted cannon fodder to elite soldiers fully capable of holding back enemy advances on their own. However, their main strength is their tanks.
They are protected from heresy and treason by two groups- the Inquisition and the Arbites. Arbites are effectively FBI, but with power armour, licence to kill anyone they damn well please, and are based throughout the Imperium. They enforce the law without mercy. They also conduct culls to maintain the population of a hive world at controllable levels, which basically means they go into the underhives and shoot several hundred thousand people, then go back for coffee and donuts and call it a day. The Inquisition are basically Arbites but without the mercy or compassion for people. They are above and beyond the law. They alone have the jurisdiction to order the destruction of a planet, known as Exterminatus.
The Imperium also has among them the Officio Assassinorum. Made of 6 clades, or groups. One clade does the electronic stuff, another works by poison, another is made to kill psykers by being unsensable by them and removing their powers, another works by brutally killing everything and everyone in the area just to make sure they got the right guy, another works by sniping, and the last works by infiltration and disguise such that they actually alter their own bodies.
They also have death cult assassins, who make their act of worship to the Emperor by killing his enemies.
Attached to the Imperium is the Adeptus Administratum. Think of the greatest amount of red tape in government work you could possibly imagine, and know that the Administratum is far less efficient than that. They make sure everyone pays their taxes.
Next comes the Adeptus Mechanicus. This is allied to but not controlled by the Imperium. They are the Tech Priests. They make things work by rituals. They're on the quest for knowledge, which involves finding an intact STC, not doing tech heresy like science or the like. They operate the Titan Legions. Think Mechwarrior, then think that the battlemechs are small compared to Titans. Their scout ones have as much firepower as the Battlemechs do. Large ones have huge ranges and the firepower to simply wipe cities off the map, as if they had never been there. They also maintain all the technology of the Imperium.
The Adeptus Astartes are the Space Marines. All male. All the people they 'harvest' for becoming a Space Marine are prime physical specimens, who are then indoctrinated, trained, and genetically modified to become superhuman. They can lose their heart and stay alive. They could lose both their lungs and survive. They could drink down poison as if it were water and survive. They can spit acid. They are better than humans in every single way. They can eat rocks. They can survive for several days fully awake and alert. They are faster than you, stronger than you, tougher than you. Their chest is bullet proof.
They're also not technically part of the Imperium.