Going by the original stories, The King In Yellow (the play) is linked in some nebulous and horrible fashion with the King in Yellow, an alien god whose "scalloped tatters ... must hide Yhtill forever". The King is in turn linked in some way with "Carcosa, where black stars hang in the heavens; where the shadows of men's thoughts lengthen in the afternoon, when the twin suns sink into the Lake of Hali". The King's nature, motives and modus operandi are unclear; but he occasionally appears on Earth, animating dead bodies or possessing those strange 'humans' already in thrall to him, and claiming (or reclaiming) those who have eluded him. To read the play is to be exposed to the King and to fall under his influence, going mad in the meantime.
The King doesn't strictly appear in the original stories, at least not in any way that allows us a good description. True, he appears to the narrator of The Yellow Sign briefly before he dies, but he is unable to convey quite what he sees.
References to the King
There are few direct references to the King in Yellow in the book that bears his name by Robert W. Chambers. There are implications that he (or it) is some kind of terrible, perhaps almighty being, of vast and insidiously penetrative reach, although it is unmentioned of just what substance or origin nor the true form it takes. Its machinations, though, appear born of a limitless desire for domination. As noted by Mr. Wilde in The Repairer of Reputations:
"The ambition of Caesar and of Napoleon pales before that which could not rest until it had seized the minds of men and controlled even their unborn thoughts ... He is a king whom emperors have served."
The tantalising fragments given of the play script, as mentioned in the stories, suggest that the King is connected with The Stranger in the Pallid Mask, who is possibly a projection or avatar of the King himself or at least his servant or emissary. The King seems, however, to be present in the 'reality' inhabited by the protagonists of Chambers' tales as well as within the fictional (to them) universe of the play's setting; part of the horror in the stories is the way the King's malice bleeds through from one layer to another. For those characters, to allow their minds to become open to the forbidden play and its world is to allow his grasp to stretch into theirs. The King's ability to possess the bodies (not necessarily still living) of those who have fallen under his thrall is evidenced by the fate of narrator Mr. Scott in The Yellow Sign:
"The gate below opened and shut, and I crept shaking to my door and bolted it, but I knew no bolts, no locks, could keep that creature out who was coming for the Yellow Sign. And now I heard him moving very softly along the hall. Now he was at the door, and the bolts rotted at his touch. Now he had entered. With eyes starting from my head I peered into the darkness, but when he came into the room I did not see him. It was only when I felt him envelope me in his cold soft grasp that I cried out and struggled with deadly fury, but my hands were useless ... I knew that the King in Yellow had opened his tattered mantle and there was only God to cry to now."
The Encyclopedia Cthulhiana says...
An avatar of Hastur, or possibly Nyarlathotep, who is the title character of [the] play. The King In Yellow usually takes the form of a gigantic human dressed in tattered yellow robes, occasionally with wings or a halo. It usually wears the Pallid Mask which conceals the hideousness of its appearance. Worship of this being has increased dramatically in recent years, and many artists and intellectuals have fallen under the King's sway.
It's worth noting that many 'appearances' of the King are the results of his appearance as a major character in a few Call of Cthulhu scenarios. The mention of wings and a halo are presumably based around a cover illustration of one of the older versions of Chambers' book.