There are at least two senses in which we can interpret the kabbalah as a psychological theory. On the one hand, kabbalistic practice could delve into the innate structure of the human understanding of the world; on the other, it could harness the cognitive power of signs which have been imbued with meaning by human culture.
1) Kabbalah as Innate Structure ~ One way to interpret the Tree of Life is as a map of the different parameters along which interior life can vary. Compare, for example, with the Myers-Briggs personality test. Myers-Briggs uses four parameters with which to measure personality types. Each parameter is defined by its extremes, for example "thinking vs. feeling," or "extraverted vs. introverted," and the test determines where on the continuum between these extremes the subject falls. Now, each Sephirah on the Tree of Life is associated with a distinct set of emotions and types of behavior: Geburah with judgment / anger, Hesed with fatherly love, Binah with motherly love, Netsah with endurance, Tif'eret with beauty / compassion, etc. These emotions / drives exist innately in every human being and kabbalistic practice allows the kabbalist to "get in touch with" these aspects of his inner life.
Of course, personality isn't exactly right as a gloss on what aspect of innate human structure the kabbalah analyzes, but perhaps the Sephiroth can be thought of as more like aspects of innate human spirituality. Those feelings within us which get triggered in church or through meditation, those passions which transcend rationality and drive us to commit selfless acts or even the most vile depravities, that part of the human mind which seeks out the supernatural, not for its plausibility, but for its possibility. The hypothesis here is that the kabbalah offers a map to one facet of innate human structure, that associated with a particular type of experience and attitude toward the world. This hypothesis is consonant with one interpretation we gave of traditional kabbalistic practice, namely as a form of meditation for discovering the aspects of the divine within oneself. The efficacy, then, of kabbalah (such as it is) could be attributed to the accuracy of this map in describing the innate spiritual tendencies latent in every human being.
2) Kabbalah as Semiotic Technique ~ The more popular account, and the one more consonant with modern, "chaotic" magickal practice, is that of kabbalah as a system for organizing signs by their significance, a semiotic toolbox, as it were. The idea is something like this: signs are powerful, they can have a profound effect on us (think of the swastika, the cross, the US flag, etc.). Each Sephiroth has a cluster of signs associated with it, these clusters being defined by some common effect or purpose. When the magickal adept "travels" to a Sephirah or the traditional kabbalist meditates upon one, all the associated signs combine in their effects to create a particular mood / emotion / state of mind far more profound than any of the signs in isolation. This rather Jungian interpretation implies that the kabbalah is contingent and a posteriori, it is a classification and organization of the by-products of human culture.
Even the semiotic interpretation of kabbalah depends on some theory of innate psychological structure. It is in virtue of this innate structure that signs effect us in the first place, and that the techniques employed by kabbalists are efficacious. The kabbalist uses his own innate susceptibility to the power of signs to rewire, as it were, his own emotional structure. By visiting a particular Sephirah (an act effected by meditation on the appropriate symbols), the kabbalist stimulates the emotional state / world view associated with that Sephirah. After the ritual, the kabbalist is a different person, in the sense that certain aspects of his worldview have been altered. Furthermore, if the reports of magickal adepts can be trusted (and insofar as they represent a subjective diary of inner states (rather than an objective account of changes in the world), let us suppose they can), the change in the kabbalist's personality can be of a variety of types. Visiting a Sephirah is not an unambiguously positive experience. While it will change the adept's attitudes and emotional structure, it will not necessarily do so in favor of the emotions and perspectives associated with that Sephirah. Basically, the adept, by performing the appropriate ritual, puts himself in a highly receptive state; in virtue of meditating upon the set of signs associated with a Sephirah, he perceives himself as present in an actual location, sometimes even conversing with entities, associated with that Sephirah. In this hightened state, however, the adept can have any number of experiences, often violently negative, and it is the nature of these experiences which will determine how the adept's psychological makeup is rearranged after the experience is concluded.
Obviously, once the kabbalist moves in his expectations past mere personal development to the alteration of the external world, he must likewise move past the psychological interpretation to some metaphysical interpretation of kabbalah. Nevertheless, it is surprising just how much of kabbalistic practice can be accomodated by a purely psychological theory, and how much of kabbalistic literature retains its interest and force in light of this naturalistic interpretation.