It's a higher form of existence or technology, but not one beyond the realm of science. Beyond our current understanding of science, sure, but not to the point of simply "unexplainable magic".
I cite two references that backup the idea of The Q being simply more advanced, not magical. One, in Q's second appearance, in "Hide and Q", Q admits that humans may one day become as advanced, if not more advanced, than the Q:
Q: We discovered instead, that you are an unusual creature in your own limited ways... ways which in time may not be so limited.
Riker: We're growing. Something about us compels us to learn, explore...
Q: The human compulsion. And, unfortunately, for us, a force that will grow stronger century after century, eon after eon...
Riker: Eons! Have you any idea how far we'll advance?
Q: Perhaps in a future you cannot yet conceive... even beyond us.
Secondly, when the Q eventually known as "Quinn" visited the USS Voyager, in the episode "Death Wish," he and Tuvok had a discussion in which he revealed that the Q are not without their weaknesses, not all powerful:
"Quinn": But you mustn't think of us as omnipotent. No matter, what the
Continuum would like you to believe. You and your ship seem incredibly powerful to life-forms without your technical expertise. It's no different with us. We may appear omnipotent to you, but believe me, we're not.
It seems clear that while the Q are amazingly powerful, powerful to a point where 21st (or 24th) century humans can't even accurately conceive, they are not magical or mystical. They have limits, and they have learned over time how to manipulate the laws of reality in ways that we simply have not yet.