I like to leave it vague. A telepath I played once firmly believed that psionic powers were connected to a hindu-esque universal mind that underlies all reality, of which individual minds are merely small parts. The world is an illusion, and furthermore a corruption of the perfect universal mind that has caused this fragmentation, pinching off individual minds like a bubble pinches off a bit of air. Introspection can allow one to make a connection back to the universal mind, and from there the seeker can do things like make contact with other minds, reconstruct one's personal reality, and affect the corrupted reality which is itself part of the universal mind, since all things are part of the universal mind.
This does tie into dreams a bit, because the physical world is merely a dream of the universal mind, which is why the seeker can change it.
However, this monist perspective was only one character. I generally leave the origin of psionic powers out of the canon of my games, because I like it to be mysterious and open to interpretation. The funny thing is, it always works, no matter why you think it works, even though the system is based on a philosophical introspection exercise, which tells you something very important about the power. I suppose I'm inspired to a certain extent by Mage: The Awakening, in which reality corresponds to belief, and not vice versa. However, that leaves questions about what exactly is the meta-reality underlying the realities that make various approaches to psionics possible. This is exactly the sort of philosophical question I want to direct psionic characters toward, when they realize that their way is not the one true way, even though there should only be one way due to contradictions that would arise if it were otherwise.