Abaddon was originally the First Captain of the Sons of Horus, having fought many battles in the Horus Heresy. When Horus was defeated at the Siege of Terra, though, the Traitor forces retreated into the Eye of Terror. With the legion now broken and without a leader, many broke off into other war bands until Abaddon reformed the Sons of Horus into the Black Legion, and cemented his leadership by launching the first Black Crusade.
There have been thirteen Black Crusades in total; originally they were all attempts to seize Cadia, the only secure way out of the Eye of Terror, but this has since been retconned. Each Crusade was a separate operation with its own goals; in the twelfth Black Crusade, Abbadon obtained the Blackstone Fortresses, which he used in the thirteenth Black Crusade to smash Cadia's pylon network and allow the Eye of Terror to expand. His ultimate goal is to eventually reach Terra and finish what his father started by killing the Emperor.
Abaddon had Fulgrim call up Lucius the Eternal to tell him that he was "having another one of his huge parties,” meaning the thirteenth Black Crusade. Eldrad Ulthran saw Abaddon and his Crusade in a vision, and was forced to contact Asdrubael Vect to warm him of the impending war.
Before these events however, it is said that Abaddon the Despoiler was out walking on the ruins of Cadia when suddenly he stumbled upon a tear in space/time that led directly directly to the Throne Room of Terra. The Emperor was actively discussing with Little Kitten, seemingly in the middle of a segue about the Adeptus Mechanicus's inability to update their technologies. Abaddon emerged from the rift, smashing into Kitten and interrupting the exposition. Ensued a confusing exchange where Abaddon introduced himself loudly to no-one in particular while the Emperor tried to make sense of the situation and introduce himself as well. The cacophonous altercation stopped once Abaddon shot Kitten, prompting the Emperor to stop playing Mr Nice guy and proceed to psychically rip off the Chaos Warmaster's arms before wishing him away. Abaddon was left adrift in space, now armless. Meanwhile the Emperor and his caretaker resumed their discussion, which was focused back on the business between the Necrons and Blood Angels, a discussion which would end with the Emperor bursting into TTS laughter.