The King in Yellow is the undisputed ruler of the pocket dimension of Carcosa. Their control over the specific Ontons in the Carcosan infestation would indicate strong ties with the Continuum Forge or perhaps a lesser version of it.
The King seldom appears but is described as a figure dressed in yellow robes and wearing a yellow-gold crown. The only part of the entity visible are feet comprising of rugose tentacles. What is under the robe is not revealed, but the imagination can fill in the gaps.
Under the Robe
The King in Yellow is a colony organism of tentacular vampiric parasites. The Gestalt Mind from these parasites is responsible for the Carcosan Reality Meme (Onton) - these vermiforms are considered by some to be the ultimate evolution of the Irisian species.
Relationship to the Irisians
Some would speculate there is a relationship between Carcosa and the Irisians. Their mutual dislike suggest a long shared history.