The First Realm is home to all "mortal" creatures such as humans and other ningen, and other less intelligent creatures, such as animals, plants, and other "living creatures" (as defined by human knowledge). In short, the First Realm is reality as First Realm inhabitants are limited to knowing, as the inner workings of the Second and Third Realms are, for all practical purposes, unknowable to human consciousness.
The First Realm is actually an infinite number of "real" universes (thus explaining why they are usually called the First Realms, collectively), of which actually a very small number of worlds (though still infinite in number) actually contain living creatures. New First Realms are constantly being formed from the Second Realm, in part to offset the Rescension and destruction of these worlds by the Aeternalae and other Youkai alike, but also in response to the virtual creation of imaginary worlds in the imaginations of other First Realm inhabitants. As a result, the "fictional" worlds of Middle-Earth, Riven, Discworld, the Milky Way of The Hitchhiker's Guide to the Galaxy, and many other worlds actually do exist, though they are beyond reach of conventional First Realm technology. This is because First Realms are still completely self-sufficient universes that are impossible to jump between through normal means. Furthermore, there are a large number of First Realms created as "alternate worlds" where they are merely worlds that branch off at a nexus point with one small change. As a result, all "alternate histories" that both have and have not been proposed by authors exist, with some being extremely similar to our current universe, having no significant changes in the long run. This is often what an Aeternal is referring to when stating that time is an illusion.
The First Realm may in fact be the most important realm of the three. Without conflict there is no meaning many philosophers have said, and without meaning there is no life. The First Realm, at its best, is like a paradise for the soul. At its worst, its a polluted hellhole that is deprived of meaning. The First Realm is easily as versatile as its two counterparts. Despite the limiting first impression one might have of it, even if it isn't as fluid as them: there are many First Realms, as they compose the many worlds that one can visit with the right help. Without the First Realm, the Second Realm would be without dreams and empty and the Third Realm would become stagnant.