root of mystic is mystery!
Briefly put, a mystic is someone who has had a personal experience with God, typically referred to as a "one-ness" with God. It can also include people who have successfully disciplined their left-brain into a non-functioning state, to produce an effect of right-brain only processing which is a roughly mystical state of mind. See Jill Bolte Taylor's stroke of insight | Video on TED.com
It can also include people who haven't had the experience, but are trying for it.
Links that might help:
Mysticism - Wikipedia, the free encyclopedia
The Christian Mystic Explained
What is Christian mysticism?
The Mystical Gnosis Event and the atheist
That last one is really interesting. The guy was and is an atheist. Just about made me cry when he describes seeing the old bearded guy.
"All it takes is for us to get a little bit self-important and narrow-minded. Toss in a little fussiness, a bit of dogma, and a bunch of pride and you've got yourself a bunch of people who wouldn't recognize the truth if it sat on them."
-- Robert Kirby