I can give you about eleven answers to this and if you'd asked Jack eight times, you'd have gotten eight more. Len Wein, who worked at DC at the time, says that it was a cover blurb intended to only appear on the covers of the fourth issues. It referred to the fact that every issue of a Kirby comic was like a world unto itself; ergo, each #4 was a "Fourth World." Folks then adopted it to refer to the whole epic that flowed betwixt Jack's books. Meanwhile, Steve Sherman — who worked with me as Jack's assistant at the time —recalls Jack coming up with it as a variation on the term, "The Third World," as used in a socio-economic context. It was Jack's way of transcending that term, as Jack transcended everything.
That may be true but I don't recall that. Apparently, Jack also told a few folks that he considered the material his fourth universe in comics. The Marvel books would have been "Kirby's Third World" and I've never quite gotten clear what the first two were. There are other answers, even less credible. Personally, I buy none of them. I don't think there was any logic behind it, at least when Jack first used it. I think it was just a term that popped into his head and he liked the sound of it. Later on, he came up with several different retroactive explanations.