The script is no help whatsoever.
Q1: The Continuum is prepared to do you a little favor... if we approve of your ruling. Look out the window.
She reacts, goes to the window.
-HER P.O.V. Out the window... she can see Earth.
JANEWAY: (whispering) That's... Earth.
Q1: Now you see it. Now you don't.
She glances away, toward him, and when she looks back to the window.
HER P.O.V.-NOTHING BUT STARS
Given that Q is essentially omnipotent, it's certainly possible that he took the Voyager to Earth but cloaked (no mention is made of its arrival and disappearance later in the show when Voyager makes contact with Earth).
It's also possible that he moved Earth to the Delta Quadrant, then erased the memories of Earth's entire population or that he copied the Earth molecule-for-molecule just for the effect, then banished it into nothingness. More than likely though, it was just an illusion of some sort. He's made those before.
Then again, this is someone whose plan to deal with an annoying planetoid was to change the gravitational constant of the entire universe.