The Kaijujin are not physical beings - they are the essential spirits of what it is to be Kaiju. They define kaiju, and the existing of kaiju define the Kaijujin. They are sentient beings who manipulate the physical world through subterfuge and indirect action - much like the ancient Greek pantheon. But the Kaijujin are not gods - though the distinction is a subtle one.
The Kaijujin are primarily concerned with the creation & battle of kaiju across the universe and beyond. They ensure that all kaiju are of similar size, weight, and power - because that makes the battles more interesting! Each of the Kaijujin represents one of the four essential elements that define a kaiju: Ferocity, Fortitude, Agility, and Power.