"I have nothing to offer but blood, toil, tears and sweat."
- Winston Churchill
"The day of small nations has long passed away. The day of Empires has come."
The Great Crusade was an important event in the history of Warhammer 40,000, seeing the formation of the Imperium of Man and reunification of humanity, and is basically the best time to be alive - If you are a loyal subject of the Emperor, that is. If not, you are endangered by just being in this galaxy, and try as hard as you can to stay out of the Imperium's reach until they are done with their megalomanic crusade.
The Emperor Emerges
For much of the 20,000's, Terra and the other human colonies were driven by war after the rebellion of the Iron Men, an era later known as the Age of Strife. The techno-barbarians (UNTZ! UNTZ!) ruled little fiefdoms on once-proud Terra, and all seemed lost.
Then, the Emperor of Mankind appeared in M28, and started conquering Terra, piece by piece. His army consisted of the first generation of Space Marines, the Thunder Warriors, using powered armor that wasn't even void-sealed (although they still had massive pauldrons). This was approximately the time that he decided that religion was bad for humanity and violently implemented the Imperial Truth, the conclusion of which can be seen in the story The Last Church.
The Next Step
Of course, Terra wasn't enough for the Emperor; he wanted to rule over all of Humanity. He had already arranged for the Void Dragon to be sealed on Mars so that, by this time in history, he would have the Adeptus Mechanicus to build awesome weapons for his armies, and now he needed some armies to wield those weapons. And to lead those armies, he needed generals, so he started the Primarch Project in M29, creating twenty super-human warriors, his sons, and his generals. The Gods of Chaos perceived this project to be a threat to them, so they scattered the Primarchs throughout the galaxy, but the Emperor had enough data to create his Space Marine Legions based on their DNA, what would later be called the First Founding (and was at the time known as the Only Founding). He sent the Legions out to find their Primarchs, and to re-unite the human colonies as they went.
The Age of the Imperium
Over the course of the next two hundred years or so, the Space Marine Legions found their Primarchs, and the Imperium of Man grew, world by world, until it spanned almost the whole galaxy. Many Xenos were exterminated along the way, as well as non-Imperial human civilizations like the Interex as the Emperor believed them to be a threat to his dominance. Between this directive and the influence of his Slaaneshi daemon blade, Fulgrim wiped out many Eldar worlds, which resulted in mutual animosity between the Imperium and the Eldar for millennia to come. Of course, considering the Eldar had been frequently raiding human worlds throughout the Age of Strife, tough shit. It was generally considered a pretty fun move on Fulgrim's part. To be fair, though, nearly all the xenos killed had descended upon human worlds during the Age of Strife and turned them into "Nightmare Worlds". As you might imagine, the crusading Imperium was not amused. In fact, most worlds added to the Imperium were of this sort, which went a long way to entrenching humanity's hatred of all things alien. Even the Jovian(for reference, Jupiter) colonies in the Sol system were pretty much horror-infested hellholes ruled over by incalculably cruel alien overlords. While Eldrad tried to contact the Emperor to warn him that he should be more concerned with stopping Chaos than with expanding the Imperium, the Emperor refused to listen to him. Both because Eldrad ordered his forces to attack Fulgrim upon realizing the Primarch was corrupted without realizing that A) Fulgrim was not yet corrupted by the sword and could still be saved and B) attacking a Primarch is unbelievably stupid if you want to live. It didn't hurt that the Emperor's creation of the Imperium was performed in a way crafted by Him to specifically act as an anti-Chaos civilization by virtue of being not only massive but also atheist. Shame he didn't realize faith hurt Chaos until the very end of the Horus Heresy. Besides, Eldrad's orders were the reason for the Eldar's raids. Not something that screams trustworthiness.
After the Ullanor Crusade, the Emperor announced that he was returning to Terra, saying that his sons were to prove that they were the leaders he had made them to be, and appointed Horus, Primarch of the Luna Wolves, as Warmaster of the Great Crusade, and withdrew to the Imperial Palace. In truth, the Emperor was ready to begin his next phase of star travel, creating a Webway portal under the Palace using the Golden Throne. Unfortunately, the Emperor's detachment from humanity created a great deal of rivalry and resentment among his sons, and his failure to fully explain matters to his sons only exacerbated the situation. The Ruinous Powers were quick to take advantage of these weak spots, and slowly but steadily began to corrupt some of the Primarchs.
This culminated with the Horus Heresy.