Not much is known about the King in Yellow save that he's the ruler of Carcosa and that a glimpse of what lies behind his mask is believed to be enough to drive anyone mad.
After she uses the Silver Key, Penny finds herself in a dystopian future where he took over our world with the help of an army of lizard people (Penny and the Silver Key Part 1). The King in Yellow has scientists working for him, including Dr Svenson, but his goals remain unclear. In Penny and the Silver Key #3, Penny learns that he's powerful enough to take out the Order and all world leaders without much effort. (She learns other things, but we can't spoil everything, now, can we?)
INSPIRATION
The King in Yellow was taken from Robert W Chambers's book of the same name. Chambers never quite explained who or what the King in Yellow and the maddening play were, though there were clear Biblical connections. While this King is mysterious, he's less godlike than the literary creation that inspired him.