A Black Crusade is an incursion that is formed when the usually disparate forces of Chaos unite under a particularly strong Chaos Champion and go forth en masse to wage war against the Imperium of Man.
Following the devastating events of the Horus Heresy, the Imperium began the Great Scouring, a campaign to cast out all traitors who had sided with Chaos and drove them into the warp storm known as the Eye of Terror. There, the followers of Chaos began to fight among each other for domination and territory and their vast armies eventually fractured.
Even so, the threat the exiles posed was far from gone. To this day they seek to overthrow the Imperium, launching separate raids and invasions against it. Once or twice within a millennium however, an exceptional Chaos Champion rises who is strong enough to bring his fellow warlords and their hosts under his sway. When this happens ancient rivalries are set aside and uneasy alliances are forged, clearing the way for what is called a Black Crusade.  
The forces and fleets that gather for a Black Crusade are made up of all types of Chaos servants: the multitudinous hordes of the Lost and the Damned, ancient and towering Chaos Titans, the bizarre war machines of the Dark Mechanicum and the Daemons of the warp. Leading them into the realm of man are the vengeful warbands of the Chaos Space Marines. 
When the crusade is launched, whole worlds fall prey to the rampaging hordes and the Dark Gods themselves divert their attention to the material realm, delighting in the sacrifices made in their names. Still, the nature of Chaos is fickle and unless it is repelled by the defenders, the crusade is bound to splinter into separate hosts and warbands who pursue their own ambitions.
The Black Crusades of Abaddon the Despoiler
The most infamous Black Crusades are those led by Abaddon the Despoiler, Warmaster of the Black Legion and successor to Horus. So far, he has led thirteen such attacks, which ranged from small raids to battles that spanned entire sectors. His latest Black Crusade, the Thirteenth, has gained him a foothold in space around the Cadian Gate. As of now, bitter fighting continues on the remaining worlds that have managed to withstand his invasion.
- 781.M31, beginning of the 1st Black Crusade aka The First Battle of Cadia.
- 597.M32, beginning of the 2nd Black Crusade a failed attack on defences of Cadia.
- 909.M32, beginning of the 3rd Black Crusade.
- 001.M34, beginning of the 4th Black Crusade. Destruction of the Citadel of Kromarch on El'Phanor.
- 723.M36, beginning of the 5th Black Crusade.
- 901.M36, beginning of the 6th Black Crusade.
- 811.M37, beginning of the 7th Black Crusade aka the Ghost War. The Blood Angels are slaughtered at Mackan.
- 999.M37, beginning of the 8th Black Crusade.
- 573.M38, beginning of the 9th Black Crusade.
- 001.M39, beginning of the 10th Black Crusade aka the Conflict of Helica. Iron Warriors fight the Iron Hands at Medusa.
- 301.M39, beginning of the 11th Black Crusade.
- 139.M41, beginning of the 12th Black Crusade aka the Gothic War. Abaddon the Despoiler tries to capture the Blackstone Fortresses.
- 999.M41, beginning of the ongoing 13th Black Crusade. Major attack on the Cadian system.
Other known Black Crusades
- The Black Crusade of Tallomin. Daemon Prince Tallomin leads an attack that is crushed by the Space Wolves.
- The Black Crusade of Doombreed. Doombreed, Daemon Prince of Khorne, declares war upon the Adeptus Astartes. The Warhawks and the Venerators are lost.
- The Black Crusade of Jihar the Lacerator. Jihar the Lacerator, champion of Slaanesh, invades Imperial space but is met by stern resistance from the Mordant 13th Acid Dogs regiment of the Imperial Guard.
- The Blackstar Crusade. In M34, Lord Ekrak, a champion of Khorne, leads a crusade to conquer the world of M'Laar XIII and ascends to deamonhood. In the aftermath, the forces under his command begin to fight each other for possession of the planet.
- The Black Crusade of Furion in M41 led by the Lord of Khorne Furion.
- The Black Crusade of the Destroyer
- The Primarch of the Imperial Fists, Rogal Dorn, was killed while stopping a Black Crusade by an unknown force sometime after the Horus Heresy
- 1: Liber Chaotica: Khorne, [Needs Citation]
- 2: Codex: Eye of Terror, pg. 9
- 3: Tactica Imperialis, [Needs Citation]
- 4: Warhammer 40,000 4th Edition Rulebook, pg. 136
- 5: Codex: Chaos Space Marines (4th Edition), pgs. 24, 46
- 6: White Dwarf 246 (US), "The Powers That Be" by Jonathan Green
- 7: Index Astartes II - The Emperor's Fists