The Harbingers, also called the Four Horsemen of The Apocalypse, are bosses which can be encountered instead of a traditional boss once the player has beaten the game for the first time (killed Mom). Conquest, however, is unlocked by blowing up 30 Tinted Rocks.
Each horseman will only spawn in its designated stage and floors after The Womb.
Every horseman will drop a Cube Of Meat or Ball Of Bandages upon defeat, except for Headless Horseman who may replace the Cube Of Meat with A Pony, and Conquest who will almost always drop the White Pony. The Cube Of Meat obtained is not re-rollable with The Dice unless the Horseman is found as the first boss of an XL Floor. Also, defeating any of the four Horsemen for the first time will unlock the Book of Revelations.
The horsemen can also appear as normal enemies in the later stages (Sheol, Cathedral and The Chest). It is possible to meet multiple horsemen of any combination in the same room, including champion varieties.
If the player has Wrath of The Lamb installed, all of the Harbingers except Conquest and Headless Horseman have a chance to be replaced by Champion versions of themselves.
If The Book of Revelations is used at least once in a level, the player is guaranteed to face a harbinger instead of the normal level boss. This is only possible if you have not met the harbinger before. For example you cannot use The Book of Revelations to replace a Basement 2 boss with Famine if you have already fought it in Basement 1.
The Book Of Revelations does not summon a horseman due to fixed bosses on the following levels:
The Depths 2 / Necropolis 2
The Womb 2 / Utero 2
The Dark Room
The Headless Horseman is another Harbinger added by the Halloween Update. He has a chance of replacing any of the four horsemen and thus it is even possible to meet him more than once during the same playthrough.
Like the other harbingers, multiple Headless Horsemen can be met in Sheol. The Headless Horseman may also be encountered as a normal enemy in the Necropolis and any floors below as only the head and may spawn in groups of as many as three at a time, especially in Sheol.
Conquest is a horseman that was added in the Wrath of the Lamb DLC. He appears as a possible replacement for Death in The Womb. (Although he is functionally an alternate version of War) Upon defeat he will typically drop a White Pony.
The concept sketches for the 4 original Horsemen in the Artbook.
The achievement for unlocking the Harbingers
The Harbingers as seen in the credits
This interpretation replaces Conquest with Pestilence (i.e. infectious disease), and is generally espoused by those unfamiliar with the actual Bible texts which describe the Four Horsemen. Though it is apocryphal, this interpretation remains most commonly used as the basis for popular culture's uses of the Four Horsemen concept, including the famous woodcut by Albrecht Dürer.
Amusingly enough, Conquest was later added in the Wrath of the Lamb DLC.
The Book of Revelation is the book of the Bible where the historical four horsemen of the apocalypse appear, explaining why holding the item increases their spawn rate.
If a Horseman is fought as the first boss on a Labyrinth floor (Excluding Conquest as he does not drop a cube of Meat), the item from the second boss will turn into a Cube of Meat if rerolled with the D6. This allows the player to accumulate a Level 4 and Level 3 Meat Boy in one run if all floors are Labyrinths and the D6 is kept. Also, the Cube of Meat from the Horseman on the first boss can be rerolled into an item from the boss pool of the second boss. It also works the same if the Horseman will be the second boss. But, it is unpredictable if the next boss is a horseman except if you used the Book Of Revelation at that floor, and the first boss item must be rerolled to get the Cube Of Meat instead of the second boss (The Horseman).
"The Bandage" - Kill 4 Horsemen of the Apocalypse in a single playthrough.