The Black King is one of the two rulers of Derse and the counterpart to the Black Queen.
Like the Black Queen, White King, and White Queen, the Black King corresponds to the chess piece with the same name.
While the Black Queen manages the affairs of ruling on Derse, the Black King leads armies in battle against the White King on the battlefield in Skaia. While Prototyped, the Black King towers over nearly all of his soldiers, standing several times the height of even the Black Rooks. Unprototyped, however, the Black King isn't too much larger than an average Pawn. This may be in reference to how in an actual game of chess, the King's playing piece is physically about 1.75 times larger than a pawn as well as being much more important, but the King's move set is almost the same (Pawn can move one space at a time in the forward direction, and the King can move one space at a time in any direction).
In a normal game session, the Black King initiates The Reckoning, causing meteors to rain down on Skaia and beginning the final 24 hours of the game during which the players must defeat him and the Black Queen.
Hivebent
Karkat explains to John that the trolls had to fight a Black King with twelve monstrous prototypings that they barely managed to kill in time.
All the troll players participated in the battle, but most important of the twelve were Aradia, whose multiple duplicates from various failed timelines repressed the psychic abilities he obtained from the Gl'Ggolyb's prototyping and turned the meteors from the Reckoning into weapons against him; Gamzee, whose Bard of Rage powers surfaced for the first time unexpectedly in this battle, dealing more damage than any of their other attacks (with the possible exception of Vriska's); and Vriska, who rolled the highest possible roll available to the Fluorite Octet, dealing the final blow. The king's scepter was thus destroyed.
The song Rex Duodecim Angelus ♫ (meant to translate to "King of 12 Angels") on the Alterniabound album puts the fight between the Black King and the trolls into music featuring each troll's theme as well as a new "King" theme. The progression is: King (0:00-1:35), Karkat (1:35-2:03), Terezi (2:03-2:32), King (2:32-2:56), Tavros(2:56-3:15), Kanaya (3:15-3:34), Equius & Nepeta (3:34-3:54), Feferi & Eridan (3:54-4:13), King (4:13-4:37), Sollux & Aradia (4:37-4:56), Gamzee (4:56-5:13), King (5:13-5:31), Vriska (5:31-6:26).
Homestuck
In the kids' session, the Black King had to deal with a rebellion of the pawns led by the Warweary Villein. However, he was quickly slain by Jack Noir. Jack, with the augmented powers of the Black Queen's ring, flew down and cleaved his scepter in two, removing the King's prototypings, then decapitated him with ease.
Post-scratch
In the post-scratch human session the Black King (or maybe just his representation) was killed early on, when the Courtyard Droll blew up the unprototyped Battlefield.