There is a form of Jewish mysticism called “Kabbalah”. There is also a Christian form of this, called “Cabalah” or “Christian Kabbalah”. What is specifically Christian about Christian Kabbalah? How does it diverge from its Jewish roots to give a specifically Christian flavour to this form of mysticism?
As luck would have it, last year I read the theses of Giovanni Pico della Mirandola (1463-1494), who tried to integrate Kabbalah with a broadly Christian worldview. I don't know how much his approach is typical of later Christian use of Kabbalah - it strikes me as rather idiosyncratic, though I wouldn't be surprised if other writers followed his basic line of thought. I'm afraid I don't know enough about Kabbalah to identify specific differences between Christian and Jewish practitioners; my impression is that they are doing the same sort of thing at a broad level, even if their conclusions are different.
For Pico, recall that the scholastic project, associated par excellence with Thomas Aquinas and Albertus Magnus, was an effort to provide an integrated system of knowledge encompassing Christian revelation, classical philosophy, and the laws of nature. All of these present aspects of the divine law. Scholastic procedure is based on rational dialogue about texts and authorities, including the Bible, certain truths accessible to human reason, and the world itself. (For the universe as a book, compare Galileo in Il Saggiatore, though the concept is much older.) The method "works" - it allows us to learn true things and reject false things - because our reasoning faculties are founded in the divine order.
One of Pico's aims was to add Kabbalah into the mix. He saw it as a unique and powerful form of knowledge, revealed to Moses by God. It was intimately connected to the structure of the natural world, and to the Bible text, through gematria of the Hebrew language, and other forms of numerology. I think that for Pico, Kabbalah was not about the mystical journey of the soul; it was more like a new intellectual tool that could be applied to philosophical and theological problems. His "Cabalistic conclusions" (the last section of the Conclusiones sive Theses DCCCC) asserts that Kabbalah is a practical form of metaphysics (3rd thesis), and can only be worked through rational intellect (12th thesis). He thought that anyone who follows his procedures would be forced to admit the veracity of Christian doctrine on the Trinity and on Jesus, just as one is persuaded by any argument in scholastic disputation (5th thesis).
An example is the 32nd thesis, deriving a reference to Jesus from three OT texts (with my translation):
We see that the passage in Genesis 49, commonly understood as Messianic, is connected through a "Kabbalistic" hermeneutic to two other verses which both contain two aleph letters. The link is meant to show that the Messiah foreseen by Jacob is identified with Wisdom (the "me" of Proverbs 8:22) and with the creation (Genesis 1); this means he has to be a Messiah on the cosmic level, rather than a mere political hero. I imagine that the numerology of two alephs in three verses is also meant to indicate the two natures of Christ and the three persons of the Trinity - Pico doesn't spell this out, but it's very much the kind of thing he does elsewhere.
Pico also builds Christian interpretations into the Kabbalistic "Tree of Life". I don't know enough about the scheme to give any helpful comment on it. The whole thing is incredibly obscure - one might even say "esoteric".
In summary, this instance of Christian Kabbalah is about incorporating the "vocabulary" and methods of Kabbalah into the service of (1) Christian metaphysics, and (2) apologetics. It is seen as a sort of secret key to the way that the world works, beyond the traditional doctrinal and philosophical sources. Therefore, Kabbalistic practice is held to be useful in supporting Christian doctrine and convincing others of its truth. This obviously differs from the Jewish view.