(Note: A friend asked me for my definition of a mystic tonight. Even though I dabble in Christian Mystical thought and have had a few first-hand experiences, I do not consider myself an expert. But I was on hand, so I answered the best I could. Here follows my answer.)
A MYSTIC IS not someone who lives in the ether: a true Christian Mystic is not someone who is so "heavenly minded that they're no earthly good". Nor is a mystic someone who performs great feats of holy strength like live on a pillar for forty days or retire to the desert for the rest of their life, only living on the Eucharist. Nor is a mystic someone who has vague notions about the divine and what that looks like in the day-to-day life. Yes, a mystic may do these things: they may seem foolish to the world, they may have great acts of purgation, and seem to live in "the grey area" because they cannot adequately express their interaction with the divine. But these things alone, do not a mystic make.
TO ME, I think a mystic is someone who believes that through prayer, union with the Divine is probable, possible and to be desired. By this broad definition, I believe that most Christians are mystics by default. This world of prayer and union with the divine, though probably not thought about, is actually practiced by many Christians, whether they call it theosis, sanctification, or whatever. There are Protestant Mystics (I'm reminded of AW Tozer, especially) and Orthodox Mystics and Roman Catholic Mystics and yes, even Anglican Mystics. To them, prayer is more than just communication with the Godhead, but it is -- through Christ -- the immersion of the soul in God like (as St. Teresa put it) a drop of water in a rushing river.
AN ACTUAL EXPERT, Evelyn Underhill defined it in her book Practical Mysticism as "the art of union with Reality." I think this is marvelous! Let me explain:
SIN AND THE sinful nature is something that is not based in Reality. I think this is most clearly seen in the sin of lust. When someone looks at pictures of an illicit nature, it invokes in the viewer feelings, perhaps emotionally, but most certainly physically the idea that there is some sort of intimacy between the viewer and what is being viewed. Whereas in Reality, viewer is simply looking at pixels or the printed page or whatever. What about when a woman desires for a married man. Though he may reciprocate the feelings and actions, it still does not remove the Reality that he is one flesh with his wife.
SIN IS NOT based in Reality. What about someone who engages in gluttony? Though (in Reality) they have eaten themselves full, they still desire more, thinking that they are hungry for whatever reason. Or the sin of Pride? Someone is prideful if they have an inflated view of themselves that is not based on the Reality that they are in need of Kyrie Eleison. I think this can be shown with all the other sins, too, but I need not labor the point.
SIN -- IN ITS very nature -- is the denial of Reality. By sinning, we've mutated and distorted Reality to suit our own desires, pleasures and needs. All of them: from Lust to Pride, from Greed to Gluttony are a false world we've made for ourselves. Its as if we've built all this massive amount of scaffolding around our souls in a vain attempt to reshape Reality into what we think it should be. We've built intimacy where there is none, we value what is worthless, we've built barns and bigger barns when there should be liberal giving. Sin is a false world whose consequences are felt in our own souls and bodies and in the souls and bodies of others.
A MYSTIC, HOWEVER, strives to let God purge themselves of these false worlds -- these huge scaffoldings that surround of the soul -- through complete submission to God. Describing this in Open Mind, Open Heart, Thomas Keating writes that "Contemplative prayer is the world in which God can do anything." I think this is true: through contemplative prayer, fasting and other such practices, the mystic allows God to tear down those false worlds that he has joyfully made. Perhaps, she prays most deeply the worlds of Our Lord, thy kingdom come, thy will be done on earth as it is in heaven.
BEING A MYSTIC, therefore is all about the art of union with Reality. Both the Reality of God and the world as it truly is. The Reality that the soul is situated in the hand of God (as Julian put it) like something smaller than a Hazelnut in your own palm. Through the brightness of mystical experiences or that purgative Dark Night of St. John of the Cross there is the union with God. But also, in that Reality, there is a deeper connection with the world -- the world as it truly is. The Christian mystic sees the world for what it truly is: fallen, but being redeemed; broken, but being healed; and offering nothing, but the breaking forth for the Kingdom of God.
THEREFORE, THE MYSTIC'S priorities are vastly different than that of the average person. In storing up treasure in heaven, they are seen as foolish to the world. In their radical submission to God like a living sacrifice, they might do odd things. From a worldly perspective, they seem to live in the ether (often accused of being "absent minded professors"). Their "vague" notions are anything but an actual face-to-face interaction with that Reality. That interaction with Reality is so different from what is known, that it is confusing to those who only know the scaffolding. And by that interaction God tears down scaffolding and the mystic helps others to let Him do the same.
IN SHORT, THEY commune with Truth.