A professor at our seminary once jokingly said, "Mysticism is a lot of mist and a lot of schism." I thought you might enjoy that...more serious comments to follow.
Charlene

Everyone here probably knows that I'm a particular fan of exegesis -- especially for definition. Mostly this is because a single word only means anything in a context. The way one group uses a word at a certain time may differ greatly from the way another group uses the word later; but generally a single person tends to use words in about the same manner during his entire lifetime, with refinements more than changes. For that reason, it's good to infer from otherwise clear statements what certain words mean. It requires a bit of triangulation, but it is worthwhile.

Everything in this post comment should be interpreted through the knowledge of that bias.

Having said that, I'll say also: I have thought a fair bit about the nature of "Mystery" -- not as much as some other important things, but a bit over the past three or four years. In what follows, I'll rely upon the grace and insight of whomever is reading to understand that a somewhat "clinical" treatment of a word used to refer to something that seems (at first blush) to be anything but clinical isn't an affront in either intent or effect. I hope that will be apparent.

In my own study of it, I have been primarily concerned with the new testament authors because in life, I am primarily concerned with "the mystery of Christ." I choose to understand first what mystery means in terms of the mystery of Christ and the news preached in the New Testament. It seems that Paul and John are the only two who use the word ("ΜΥΣΤΗΡΙΟΝ"), although Peter alludes to the fact that Paul has great insight into things hard to understand.

Rather than build an exegetical case for my definition, I'll just say what it is. Whoever is curious can, of course, feel free to check it out themselves. If you want to ask me about it, please do -- I love to discuss the good and true things =) I'm especially interested in anyone who can give me compelling reason to change my understanding.

Anyway, to get to the point, a "mystery" (translated by some translators as "secret") is "undiscoverable truth." It's a bit of a terse definition, so I'd like to expand it a bit.

First, the truth is not able to be discovered but it is able to be known. This much is clear, since Paul claims to be able to tell others about various mysteries, and that some are known to "us." It turns out that mysteries can never (even in principle!) be discovered by any exploration, but can be known only by revelation. This is an important distinction! It classifies truth not by it's known-ness, but perspectivally. Because of this, a mystery remains a mystery when it becomes known and understood. Further, a mystery is never diminished in either its mysteriousness or import when it has been revealed -- even fully revealed -- to anyone. God is never glorified less by the understanding of a mystery, but always more because the revealed truth becomes a first principle from which to reason (obviously), and testifies to the (1) existence and (2) goodness of God.

Because there is no method for man to know a given mystery, the meaning seems to have blurred to mean "unknownable truths." Notable among this group is "the mystery of the Trinity," which many have insisted is merely beyond human understanding. But a subtle idolotry comes in when this happens: one gives the "Mystery" itself precedence over God. the Mystery of the Trinity is something that no man can possibly discover, but there is no truth unknown to God, and there is no limitation so great that He cannot overcome it. God can reveal any truth to anyone, because all truth is His, and so are we. He has complete authority and power to do as he will in this matter.

Men have sometimes confused the undiscoverability with unknowability. This, itself, stems from a misplaced faith: that human knowledge starts with man. There has also been a second difficulty (historically): when a mystery is proclaimed, it cannot be verified by others except by independent revelation which they cannot invoke, because they do not command God. For this reason, false teachers have come proclaiming untruth in the name of "Mystery." I'm sure that many of them sincerely believed it, and that some of them even received revelations from unclean spirits, mistaking them for God. This latter is most commonly what occurs in false religions. "Mystics" of Islam, Hinduism, the Babylonian religions, etc. have been given many revelations by demons and, since their claims are false they are (obviously) unverifiable. In order to avoid this problem, many Christians have thrown out the baby with the bathwater -- they have fallen into a concession that whoever claims to have an understanding of a mystery must be false -- in order to protect against the chance that it's the case.

The understanding of a given mystery is always a gift from God. It has been given to some to know mysteries and proclaim them -- we call them sometimes "mystics" and sometimes "prophets" (the events of the future, for example, are undiscoverable; but God can, and has, and does reveal it to some as He sees fit). It is a fearful thing to receive a revelation from God -- and the first such revelation any man receives is the revelation of the Mystery of Christ: that Jesus was the son of God, in very nature God, born in flesh, to bring salvation from death, by death, by grace through faith in this very mystery. After this, the God who lives and loves continues to reveal to his children the good and true mysteries. But, as I said, this is a fearful thing. Lacking in wisdom, some have spoken foolishly about what has been revealed to them, and suffered shame for it. Others, also lacking wisdom, have been proud -- as if by their own power the knowledge has come to them -- as if the mystery were merely undiscovered by men, and not undiscoverable. When this happens, men bring the discipline of God upon themselves. Knowledge of a mystery is a fearful thing to have, because it requires much faith. As a rule, one ought not to speak of a mystery if they have not been told to; and one must speak of a mystery if told to. This is only a guide -- wisdom brings finer discernment, but if anyone is uncertain about it, this rule is good to follow.

Finally, I'll point out that there are a good many things about God that are not mysterious. That is, there are some truths about God that can be discovered by man, "for since the creation of the world God's invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that men are without excuse." But there are some truths about God that are mysterious. No one can know the persons of God without revelation. None can comprehend the incarnation without revelation. None can gain the knowledge of God that comes through fellowship with Him without his revelation of Himself to them. The mysteries of God are unnumerable and are more profound than what can be known by men. It is the great blessing of God that he should reveal himself to us -- and the delight of every believer to be "a mystic" -- one to whom God reveals Himself and His creation.

With regard to "mystical prayer," it can mean: prayer in which we pray not what we desire to pray, but what is revealed to us as God's prayer for us, through our prayer. Have you ever had the experience of speaking to another person and suddenly being carried along by the spirit in what you say and speaking from the heart of God? This is similar to "mystical prayer." Sometimes, when we pray we open ourselves to God and humble ourselves before him, and we find that it is not that we are praying, exactly, but that, in prayer, we are participating in a motion of the Spirit upon the Earth. Now, it is still our prayer as well, but only in the way that, say, a large wave can be said to be "comprised of" its component waves (remember your wave mechanics?). It is impossible to pick out one from the other -- they have fully become one -- yet it is distinct from either alone. So it is with "mystical prayer" -- it ceases to be possible to say, "this is my prayer to God," but neither is it possible to say, "this is not my prayer." In truth, it is "the mystery [i.e. the undiscoverable truth of the will] of God revealed through your prayer."

The meaning may be altered slightly in particular usages, but this is a solid foundation for a beginning of understanding. I'm not sure if this is what people mean when they say what you are hearing. My experience is that people often don't actually mean anything in particular when they speak of things in abstraction like this ... or at least, are not sure exactly what they mean. Probably some of the people you hear are all hard core about it and know what they mean and mean true and real things, and others (probably the majority?) have heard the phrase, match the notion with some not-yet-well-examined experience (that may or may not be a good fit), and have repeated it, trying to convey something of which they are not quite clear. (This last bit isn't judgement, by the way, just observation. I would prefer that such not be the case, but I have experienced that it seems to be with most similar things.)

hmm. I don't know a lot about mysticism. When I hear it used in a Christian context, I intuitively associate it with contemplation, which jives with the definition you gave in the post. Perhaps that is because mystical prayer would not be about presenting your requests and/or praise to God, but letting God reveal mysteries to you. Thus, silence and solitude also intuitively come into play in my mind's eye.

Though honestly, I don't think I've ever heard someone contemporary refer to their prayer life as "mystical." I also wonder whether the ones we refer to as mystics - like St. John of the Cross and St. Teresa as you mentioned - would use this term in describing their own experience. I have read very little of mystics, and couldn't even name another one off the top of my head, but maybe someone is more familiar and would have a clue? My guess would be no, in which case, I would question why someone nowadays would make it a point to say their prayer life is "mystical" - it seems potentially divisive.